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Book l 34 



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THE '-MECHANICAL WORLD" SERIES 



TANK CONSTRUCTION 



UNIFORM WITH THIS VOLUME 

COMMERCIAL ENGINEERING 

By "A GENERAL MANAGER" (Alfred J. Liversedge, 
A.M.I.C.E.), Author of " Engineering Estimates, Costs and 
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WORKSHOP PRODUCTION 

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THE DESIGN OF DRILL JIGS 

A Practical Manual. By A. N. HADDOW. 
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Manchester : EMMOTT & CO., Ltd., 65 King Street. 
LONDON; 20 BEDFORD STREET, W.C. 2. 



TANK 
CONSTRUCTION 

Relating principally to the Design^ Manufacture 
and Erection of Tanks in Mild Steel 



ERNEST Gi^KECK 

Wh. Ex., Assoc. M.Insi! C.E. 

AUTHOR OF "structural STEELWORK," ETC. 



MANCHESTER 

EMMOTT & CO., LIMITED 

65 KING STREET 

LONDON : 20 BEDFORD STREET, W.C. 2 

1921 

(^All rights resen.'ed) 



^ ^ S- i 2L '^ 
1 ->- 



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PREFACE 

Besides an endeavour to present information likely to be of 
use in the practical design and construction of tanks, one of the 
main objects of this volume is to draw attention to the many 
problems involved in tank construction. Properly regarded, these 
problems are so full of interesting possibilities that they become 
absolutely fascinating to the practical engineer; while their com- 
mercial importance is at once so real and so great that the field of 
study which they offer cannot prove aught but profitable. 

Present-day requirements, developments and tendencies indicate 
unquestionably the need for a more soundly reasoned basis of design, 
and more efficient, rapid and economical methods of construction, 
than have been commonly employed in the past. 

There seems to be an impression in the minds of some that our 
knowledge concerning the principles involved in the design and 
construction of tanks is more or less complete ; that the only means 
available for reducing the costs of production is by cutting down 
the thicknesses of the sheeting or omitting essential parts of the 
construction ; and that anything in the way of practical investiga- 
tion and research would be mere waste of time and energy. 

No impression could be more completely at variance with the 
facts. Instead of our knowledge with regard to the subject being 
complete, it is shown in the following pages that, in some of the 
most commonly employed methods of constructing tanks, we do 
not even know how the sheeting acts in resisting the pressures of 
the contained liquid; while it is usual to " design " the sheeting on 
a basis of assumptions which certainly and obviously cannot be 
realised in the finished structure. Instead of economy in manu- 
facture being limited to senseless " cutting " of material, it wil 
be seen by the reader that few branches of engineering can offer 
such wide and rich fields for the exercise of skill in securing true 



VI PREFACE 

economy through the more effective use and disposition of material. 
And instead of investigation being unnecessary, it is shown that 
there are several — and these but a few of the most obvious — points 
on which practical research is urgently needed. 

So far as the author is aware, no book has been published 
previously dealing with the practical design and construction of 
tanks, and it is hoped that the method of treatment here adopted 
may prove acceptable, not only to those engaged in the actual 
design, fabrication and erection of tanks, but also to many con- 
cerned with structures of a similar nature. In addition, the book 
contains much that should prove of interest and assistance to 
students of structural work generally. 

The aim throughout has been to make the treatment broadly 
suggestive, rather than particular or exhaustive, partly in the hope 
of stimulating interest in the subject, as well as showing the scope 
for individuality in providing for local exigencies and meeting 
special requirements. 

Not only has every endeavour been made to describe clearly 
and faithfully the various methods of design, manufacture and 
erection in common use ; but, in addition, it will be found that a 
considerable proportion of the book is devoted to suggestions for 
improving those methods, commercially and scientifically. The 
practical application of the various principles involved is illustrated 
by means of numerous examples, typical of ordinary practice, 
completely worked out. 

Among the parts of the work which are believed to be original, 
attention is particularly invited to : (i) the discussion regarding 
Economy of Form, in Chapter II — especially with regard to the 
influence of floors and roofs, of costs differing materially from that 
of the walls, upon the economical proportions ; and also with regard 
to the latitude available for departure from the proportions giving 
maximum economy in the area of sheeting; (2) the suggested 
method for staying the walls of rectangular tanks by means of 
horizontal rails, in Chapter IV ; (3) the investigation concerning 
the action and design of curbs and rails, in Chapter V; (4) the 
treatment for trough-bottomed rectangular tanks, in Chapter VI ; 
(5) the suggested methods for simplifying the design, manufacture 
and erection of the roofs, walls and floors of cylindrical tanks, in 



PREFACE _ Vll 

Chapter VII ; and (6) the treatment for dished bottoms of elevated 
cyhndrical tanks, in Chapter VIII. 

The bulk of the work given in the following pages was published 
in the form of Articles contributed by the author to the Mechanical 
World during the years 1916-1920 ; and the author is indebted to 
the editor of that journal for permission to republish the work in 
book form. All the work previously published in article form has, 
however, been carefully and thoroughly revised, while some new 
matter has been added. 

With the object of focussing attention the more clearly upon 
the matter of actual tank construction, and also to prevent the book 
from becoming large and costly, no attempt has been made to treat 
in detail the steelwork or other construction for supporting elevated 
tanks. Some general considerations regarding such work are given, 
and particular mention is made of a few important points ; but for 
treatment of the foundations, stanchions, beams and bracings in 
detail, the reader is referred to the author's book on Structural 
Steelwork (Longmans, Green & Co.). 

The author hopes to find, in the near future, an opportunity 
for presenting a treatment of bunkers, bins and silos, on lines 
similar to those here adopted for tanks. 

Ernest G. Beck. 

London, 

October 1920. 



CONTENTS 

CHAPTER I 

MATERIALS, PERMISSIBLE STRESSES AND RIVETING page 

Introduction — Materials of Construction — Riveting generally — Setting- 
out Rivet-holes — Punched Holes — Effects of Punching — Drilled 
Holes — Nominal Rivet-diameters — Proportions of Rivets — Yard 
and Field Riveting — Faults in Riveting — Lengths of Rivets for 
Ordering — Rivet-diameters — Pitch and Arrangement of Rivets — 
Rivet-resistances — Friction in Riveted Joints — Weight of Tank- 
work — Permissible Stresses — Physical Properties of Materials- 
Effects of Manufacture — Conditions of Loading — Conditions of 
Working and Permanence — Factor of Safety — Caulking . . i 

CHAPTER II 

ECONOMY OF FORM 

Capacity in relation to Cost — Tanks Square on Plan — Proportions for 
Economy of Sheeting — Effects of Departure from Economical Pro- 
portions — Effects of Roofs and Floors upon Economical Pro- 
portions — Tanks Rectangular on Plan — Proportions for Economy 
of Sheeting — Effects of Departure from Economical Proportions — 
Comparison of Square and Rectangular Forms — Effects of Roofs 
and Floors upon Economical Proportions — Cylindrical Tanks — 
Proportions for Economy of Sheeting — Comparison of Cylindrical 
with Square and Rectangular Tanks — Effects of Departure from 
Economical Proportions — Effects of Roofs and Floors upon 
Economical Proportions — Cylindrical Tanks with Dished Bottoms 
— Conical and Hemispherical Bottoms — Economical Proportions 
— Effective Storage Depth of Sheeting — Trough-bottomed 
Rectangular Tanks — Economical Proportions • • • . 33 

CHAPTER III 

FLOORS AND WALLS OF RECTANGULAR TANKS 

Tank Floors and Walls generally — Design of Rectangular Floors — 
Spacing of Floor Joists — Determination of Plate-thicknesses — 
Arrangement of Plating — Seams in Flat Floors — Treatment of 
Main and Subsidiary Seams — Riveting in Floor Seams — Thinned 
Plate-corners — Tapered Packings — Packed Seams — Attachment 
of Walls to Floors — Cantilevered Walls — Permissible Depths for 
Stock Plate-thicknesses ....... 



70 



IX 



X CONTENTS 

CHAPTER IV 

WALLS OF RECTANGULAR TANKS pace 

Stayed Walls — Conditions of Stability — Sta3dng by means of Curbs — 
Design of Sheeting — Permissible Depths for Stock Plate-thick- 
nesses — Stapng by Horizontal Rails — Economical Level for Rail — 
Design of Sheeting — Permissible Depths for Stock Plate-thick- 
nesses — Effects of Variations in Liquid Head — Walls with Several 
Horizontal Rails — Design of Sheeting — Walls with Vertical 
Stiffeners — Design of Sheeting — Arrangement of Curbs, Rails and 
Stiffeners — Need for Research ....... 93 

CHAPTER V 

FRAMING FOR RECTANGULAR TANKS 

Horizontal Ties — Trussed Ties — Support for Ties and Trussing — Trussed 
Framing — Action of Curbs and Rails — Gusseted Corners — Design 
of Curbs and Rails — Staging for Curbs and Rails — Support for 
Trussed Framing — Economical Proportions of Tanks with regard 
to Curbs and Rails — Points of Contrafiexure — Effects of Sectional 
Variations upon Continuity — Bracketed Comers — Tied Comers — 
Design of Comer Ties — Vertical Stiffeners — Continuity of Sheeting 
— Ribbed Tanks — Raking Stays — Design of Framing — Bottom 
Corner Connections. . . . . . . . .131 

CHAPTER VI 

TROUGH-BOTTOMED RECTANGULAR TANKS 

Action of a Trough-bottom — Rib-plates and Ties — Model for Studying 
Trough-bottoms — Design and Construction of Trough-bottoms — 
Need for Research — Suggested Methods of Construction for 
Troughs — Bulkheads — Suspension of Troughs — Designing for 
Facility in Transport and Erection — Framing and Bracing — 
Effects upon Stanchions — Bracing for Stanchions . . .183 

CHAPTER Vn 

CYLINDRICAL TANKS 

General Arrangement of Cylindrical Tanks — Roofs — Suggested Methods 
for the Construction of Roofs — Floors — Suggested Methods for the 
Construction of Floors — Treatment of Circumferential Shaped 
Plates — Erection of Floors upon Solid Bases — Cylindrical Wall 
Plating — Suggested Methods for designing Wall Strakes — Seams 
and Riveting in Cylindrical Walls ...... 204 

CHAPTER VIII 

ELEVATED CYLINDRICAL TANKS 

Various forms of Bottoms — Flat Floors — Conical Bottoms — Investigation 
of Stresses — Hemispherical Bottoms — Investigation of Stresses — 
General Considerations regarding Dished Bottoms — Substructures 
and Foundations ......... 247 

INDEX 261 



TANK CONSTRUCTION 

CHAPTER I 

MATERIALS, PERMISSIBLE STRESSES AND RIVETING 

I. Introduction. — ^The storage of water and other liquids in 
tanks, below, at, or above ground level, provides some of the most 
interesting and important problems with which the practical 
engineer is called upon to deal. Circumstances and conditions vary 
widely with different types of requirements, and, indeed, often 
with individual cases of the same type, so that no rigid rules or 
methods, either for design or construction, can be of general applica- 
bility. Appropriate methods — or, at least, appropriate modifica- 
tions of some standard method — should be used to provide for and 
satisfy the special circumstances and conditions of each type, and, 
where necessary, of each particular instance. 

All methods must, of course, rest more or less upon a broad 
basis of accepted principles, as regards both theory and practice, 
if satisfactory results are to be obtained. The form and propor- 
tions of each tank should be in accordance with the established 
conclusions of mensuration, except in so far as modifications are 
demanded by local requirements and exigencies ; the stability, 
strength, and stiffness of the structure as a whole, and also of each 
part and connection individually, must comply with the laws 
of mechanics, including adequate provision for corrosion, based 
upon the results of observation and experience ; and the relative 
arrangement of the component parts needs to be such as will facilitate 
and ensure the production of an economical and efficient structure, 
by lending itself to simple and satisfactory methods of manufacture. 

It is surprising to find that these considerations, though obviously 
correct and sound from the commercial, as well as from the scientific, 
B 



2 TANK CONSTRUCTION 

point of view, are to a large extent ignored — at least, in this country. 
Apparently, special requirements and local conditions are often 
regarded as the dominating factors in design, to which all other 
matters must be sacrificed, whereas the position they should occupy 
is that of particular features of the problem, to be always properly 
met and treated, but in no case permitted to assume paramount 
importance to the exclusion or undue detriment of efficiency and 
economy. 

Sometimes, of course, the position allotted for the tank, owing 
either to lack of proper consideration in a new layout by one who 
will not be called upon to design the tank, or to insurmountable 
obstacles, is such as to render a good design very difficult, if not 
impossible ; but even so, much may be done (in the way of limiting 
the effects of the initial handicap) with care and a clear understanding 
of the principles involved. Moreover, such cases are less numerous 
than is generally supposed, and might be fewer if the facts were 
considered; but even if efficiency and economy in the design of 
the tank proper had frequently to be sacrificed, there would still 
be no reason or excuse for abandoning them. 

Were tank construction placed upon the definite basis which it 
deserves, all competent designers would agree as to the essentials 
of any proposed tank ; after providing for the local conditions and 
particular requirements of the case (which are, of course, largely 
matters of fact, and not of opinion), legitimate differences in design 
would be limited to such directions as the respective equipment 
and resources of the shops and yards which the individual designers 
knew would carry out their work if accepted, and to the skill of 
each designer in minimising the unavoidable departure from the 
established principles of economy and efficiency caused b}^ the 
special exigencies. A design which differed radically from that by 
which the most advantageous results could be obtained at the 
lowest cost would proclaim its producer either incompetent or 
lacking in proper facilities for satisfactory manufacture. Legitimate 
competition in prices would be limited to such matters as the ability 
and power to secure the best values, both in buying material and 
in methods of manufacture, the margin of profit required, and the 
cost of transport from the yard to the site, in addition to those 
resulting from the differences in design mentioned above. Clearly, 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 3 

there could not, in such circumstances, be any great divergence in 
prices, while the quality of the tank would be high, and practically 
constant, for all. 

How different would this be from (and how desirable in com- 
parison with) the existing state of affairs, in which orders are too 
frequently given for tanks designed without regard for economy 
of form, the resulting extravagance being masked by the use of 
inferior materials and shoddy workmanship, to the detriment of 
conscientious and capable designers who would give greater value 
out of all proportion to the slight increase (often only apparent, 
and not real) in cost. 

A tank nearly always requires special construction of some 
kind to support it, and the cost of the tank should be considered 
in conjunction with that of its supporting work. Tanks of un- 
economical form may (and frequently do) involve extravagance 
in the methods of carrying them, and in this way, even though the 
cost of the tank itself be reduced by means of unwarrantable and 
dangerous expedients, the actual outlay in respect of the structure 
as a w^hole may be unnecessarily increased, in addition to probable 
waste of valuable space which a better design would have rendered 
available for profitable use. 

In the following pages an attempt is made to indicate, in some 
detail, the principles which should underlie the design and con- 
struction of the various types of tanks in general use ; and to show 
how those principles may be applied in practice. Regard is paid 
to the relative importance of the various principles in various 
circumstances, and to the methods by which local conditions and 
special requirements may be met and satisfied without undue 
sacrifice of economy and efficiency; while it is also shown that 
even accepted methods of design, generally regarded as of high 
standard, have so far failed to take sufficient account of some 
important considerations, and have ignored others, which might 
well prove very useful on occasion. 

2. Materials of Construction. — Only the best materials of their 
respective kinds, and the most suitable for the purpose, should be 
used for the construction of tanks. With material of uniform and 
reliable quality, the necessary provisions for strength and stiffness, 
and allowances for corrosion and other effects, may be properly 



4 TANK CONSTRUCTION 

made in such a manner that the margins are of (more or less) known 
extent, and may therefore be rehed upon: 

Most of the material used for the walls and floors of tanks is 
comparatively thin, and slight inequalities in thickness are un- 
avoidable. A small decrease in thickness when the total nominal 
thickness is not great may involve a relatively large proportionate 
reduction in strength, even with good material. In low-grade 
material, not only are such inequalities in actual thickness greater, 
but there are also wider variations in the quality of the material, 
and thus it is impossible to rely, with justifiable confidence, upon 
the results of calculations as regards strength. 

A further objection to the use of inferior materials lies in the 
fact that they are difficult to work. Joints and seams must be truly 
closed in tank construction, and this is impossible if the plates are 
not fiat, or if holes cannot be properly formed owing to brittleness 
or irregularities in the metal, \^'here a satisfactory structure is 
required, therefore, it will probably be found cheaper, as well as 
better, to use standard materials. There are, of course, some who, 
having no reputation to preserve, care nothing for satisfactory 
results — indeed, the only result they regard as satisfactory is the 
due receipt of the contract price, highly inflated by imaginary 
" extras," — and these, recognising that all (and more than) they 
save by purchasing inferior material would be lost if good workman- 
ship were attempted, employ such other methods of manufacture 
as will, aided by plentiful red lead and jointing devices, enable the 
tank to pass muster if there be no intelligent examination or test — 
though mention of inspection and tests in a specification is usually 
sufficient to destroy their interest in the proposal. 

A tank so constructed is certain to give trouble sooner or later ; 
and once it starts, the trouble is likely to continue until the tank is 
scrapped. If those who made it be asked for an explanation, they 
reply in vague terms, darkly hinting at the existence of some 
mysterious and malignant power ^ which all their " skill and care " 
has sometimes (as in the case under question) been insufficient to 
circumvent — not because their efforts were relaxed or small, but 
because the evil one was unusually wily. With such we have no 

* The author has actually heard such foolish excuses put forward, and not 
always without success. 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 5 

concern, for the simple fact is that, apart from inevitable deteriora- 
tion or the effects of misuse and neglect, a leaky tank bears witness 
to bad material or faulty workmanship, and to nothing else. 

Some years ago, large numbers of tanks were built of cast-iron 
plates, flanged for jointing, and provided with stiffening webs 
where necessary. The skin of cast iron may render assistance in 
minimising corrosion, but the material is notoriously treacherous 
when subjected to bending actions, and this has undoubtedly 
been the cause of several failures. Moreover, although cast iron 
is cheaper than steel, it is doubtful whether a tank, of specified 
capacity, could be built for less in cast iron than in steel, for the 
jointing flanges, fillets and webs, involve a considerable increase 
in weight which is largely avoided in steel, while the meeting faces 
of all flanges on the cast-iron plates must be planed and fitted with 
accuracy and care if tight joints are to be possible, which would 
cost more than the riveting for a steel tank. It would be difficult, 
also, to fit stays in a cast-iron tank. 

Probably some few tanks, of comparatively small sizes, are still 
made in cast iron, but for general use, steel construction, consisting 
of plates riveted together, and suitably stiffened and stayed to 
resist the internal pressure, is preferred, and to such an extent that 
no attention need be paid here to cast iron as a material for tank 
construction. 

Recently several important tanks have been constructed of 
reinforced concrete, and there are undoubtedly circumstances in 
which this material seems to be peculiarly suitable. Owing to the 
thicknesses being unavoidably great as compared with those which 
would suffice in steel, the weight of the tank is somewhat seriously 
increased — with good design, the weight of a reinforced-concrete 
tank would be not less than twice that of a tank having the same 
internal dimensions built in steel, in spite of the fact that the 
weight of reinforced concrete is less than one-third that of steel, — 
but in some cases this increase in weight might be of little importance 
compared with the weight of the contained liquid. 

The principles which underlie the design for a reinforced-concrete 
tank are, however, very similar to those discussed in the following 
pages ; and as it is only in special circumstances, and under peculiar 
conditions that reinforced concrete is likely to be used in preference 



O TANK CONSTRUCTION 

to mild steel plated work for the construction of tanks, it has 
been thought well to omit discussion of such methods in detail 
from the present volume. 

For steel tanks, all material should be of British Standard 
Specification — i. e. — 

Mild-steel Plates. — Tensile breaking strength between the 
limits of 28 and 32 tons per sq. in., with an elongation of 
not less than 20 per cent, in a length of 8 in. 

Steel Rivets. — Tensile breaking strength between the limits 
of 25 and 30 tons per sq. in., with an elongation of not less 
than 25 per cent, in a length equal to 8 times the diameter. 

Wrought-iron Rivets. — To be made from bars of " Best York- 
shire Iron." Tensile breaking strength between the limits 
of 21 and 25 tons per sq. in., with an elongation of not less 
than 29 per cent, in a length equal to 8 times the diameter, 

Rolled sections {i. e. joists, channels, angles, etc.) should be of 
mild steel, to the same specification as for plates. 

3. Riveting Generally. — There are two conditions to be satisfied 
in the riveted joints of steel tanks — viz. strength and tightness, — 
and both are equally important. Economy in holes and rivets must 
sometimes be sacrificed to obtain tightness, but a good designer 
will endeavour, by means of skilful arrangement, to minimise such 
unavoidable waste. For instance, it may happen that joints and 
seams, owing to the commercial limits of sizes in plates and bars, 
occur in positions where the effects of fluid pressure are small, and 
hence the provision of riveting necessary for mere strength would 
be insufficient to prevent leakage. It will presently be shown that 
by careful and intelligent designing, the occurrence of such joints 
and seams may be limited to cases in which they are really inevit- 
able, and also that undue waste may be prevented. 

Satisfactory riveted work is both costly and difficult to obtain 
in this country, and for this reason some manufacturers regard all 
other factors in the design of a tank as subservient to the minimising 
of riveting. It is, of course, sound economy to eliminate all un- 
necessary or avoidable riveting, provided that other, and more 
important, aspects of the design are not adversely affected thereby; 
but there are, as has already been pointed out, considerations 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 7 

besides the first cost of the tank itself which maj^ not always properly 
be ignored. 

Plate thicknesses should not be less than J in., nor more than 
I in., and no rivets should be used having diameters less than J in. 
or more than J in. 

There is no simple and reliable rule expressing the most suitable 
diameter for the rivet in terms of the plate thickness ; many of 
those so far proposed give absurd results for some thicknesses — for 
instance, d = TzVt (perhaps the best-known one) is reasonable 
for thicknesses less than f in., but suggests a rivet diameter of i in. 
for f in. plates, and i J in. diameter for i in. plates, which diameters 
are too large for practical use, requiring enormous power to close 
the rivets properly. The linear relation — 

^ = 0*4 + 0-5 /, 

d being the rivet diameter and t the plate thickness, fits practical 
proportions, for this class of work, better than any other, but the 
large extent to which circumstances as regards strength and tightness 
of joints and seams vary, the small range of plate thicknesses and 
rivet diameters practicable, and the fact that rivet diameters must 
alter by eighths, or, at the least (and not too often), by sixteenths, 
of an inch, , render any such rule of little use except as a rough 
guide for a first approximation from which modification may 
commence. 

4. Setting Out Rivet-holes. — Rivet-holes, if they are to be formed 
by ordinary single punching methods, should be carefully set out 
by means of properly constructed wooden templets, which, for 
tank, work, are usually very simple. 

Multiple or rack methods may possess some advantages in 
quickness as compared with the single-formation methods, but they 
have disadvantages also in greater liability to breakage in the 
punches or drills, and the holding-up of the whole machine if one 
punch or drill breaks. Moreover, such methods are apt to involve 
limitations in the pitch and arrangement of rivets which cause loss 
of economy in the work as a whole. 

An important point (which is surprisingly often lost sight of) 
is that every rivet-hole must he filled with a rivet ; and, since the 
cost of filling a hole must be added to that of forming it, a cheap 



8 TANK CONSTRUCTION 

method of forming holes, if allowed to form more holes than are 
necessary, may actually be the means of increasing the cost of the 
work as a whole. 

The holes in the templets need not be the same size as those for 
the rivets which they locate; they are generally made to some 
convenient size (say, f in. diameter), and kept uniform for all 
templets. If the rivet-holes are to be punched, the templet is 
laid on all the pieces to which it relates, one at a time, and the 
positions of the holes marked on the steel by means of a centre- 
punch, formed to fairly fit the holes in the templet, and having a 
central projection (or " nipple ") with which the indentation is 
made. By this means, the markings on all pieces should be identical, 
no matter how many pieces there be. 

If the holes are to be drilled, only one piece need be marked 
with the punch, and this piece may then be carefully drilled to form 
a " master " for all similar pieces. A number of pieces may then 
be clamped or otherwise fastened together, with the " master " 
piece on top, and the drill sent through all thicknesses at each mark 
in one operation. 

5. Punched Holes. — If the holes are punched it is usual to employ 
a " nipple-punch " — i. e. a punch having a small conical projection 
at the centre of the circle formed by the cutting edge. The work 
is placed on the nest so that this projection (or *' nipple ") enters 
the indentation made by the centre-punch when marking-off, 
and thus it is ensured that the holes shall be formed truly in the 
positions marked. 

It has long been the practice of engineers to specify that rivet- 
holes shall be drilled, but that if the manufacturer prefer to do so 
he may punch the holes slightly (usually J in.) smaller than that 
necessary for the finished rivet, afterwards broaching or reaming 
to the final dimensions so that the material damaged by the punch 
shall be removed. 

The latter method was, until recently, standard practice in the 
best yards; and is still very generally adopted, though drilled 
holes are becoming much more common than formerly. Even 
from the manufacturer's point of view, however, there has always 
been a drawback in connection with punched holes. This drawback 
consists in a lengthening or wrinkling of the pieces along the rivet 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING Q 

centre-lines, giving additional trouble in straightening and other 
adjustments necessary before the rivets can be driven. 

6. Effects of Punching. — The material apparently shrinks from 
the punch every time a hole is formed, the consequence being that 
the bar is stretched along a row of holes. This lengthening often 
amounts to 0"i per cent., or \ in. in a length of lo ft. ; it varies, 
of course, with the thickness of the metal, the form and section of 
the bar, and the size, pitch, and position of the holes. 

Now, the first effect of this lengthening is different in different 
cases. If the bar be an ordinary flat, only a few inches in width, 
the length will simply increase; if it be a wider plate, with the 
holes close to the edges, the length will increase but slightly, if at 
all, because the main body of the plate resists stretching; but the 
strips along the lines of rivet-holes will stretch, and the result is a 
series of buckles or corrugations throughout the length. Such 
buckles are very stiff, and cannot be removed by bolting or riveting 
the pieces together ; if the rivets be driven without first removing 
the corrugations, the majority of the rivets will be rendered loose or 
otherwise defective on cooling, and the seam cannot possibly be 
rendered tight against leakage. If one limb of an angle bar be 
punched the bar will curve, the punched limb increasing slightly in 
length, while if both limbs be punched the whole bar will stretch, 
and curve about the root, in addition to buckles being formed in 
the outer portions of the limbs. 

The ultimate effect of all this is that the processes of marking, 
holing, assembling, and riveting do not follow in uninterrupted 
sequence. Nearly every piece must be straightened after punching 
as well as before marking, and, unless the length be small, further 
reaming is necessary when the work is assembled, before riveting 
can commence. 

Consider, for instance, a row of rivets connecting the floor or 
side plates of a tank with the curb angle. The angle will stretch 
more than will the plate in punching, and it is not unusual for the 
holes at the ends to be o*i in. out of line when the work is assembled. 
The rivet would not pass through such an aperture, of course, so 
a reamer must be set to work. Now, there being only the two 
thicknesses, the reamer will cant in the hole unless special means 
be adopted to support it at both ends, and the hole, besides being 



10 TANK CONSTRUCTION 

of irregular shape in both pieces (and therefore almost impossible 
to fill properly), will not be at right angles to the pieces. Even if 
the reamer be supported to keep the axis of the hole square with 
the surfaces of the pieces connected, the hole in the plate will be 
reamed on the opposite side from that on which the hole in the angle 
is reamed, making each hole oval in shape. Hence there would 
be two crescent-shaped spaces into which the material of the rivet 
must be forced if the hole is to be completely filled, which could 
seldom, if ever, be done. By commencing the riveting at the centre 
of the length, the amount by which the extreme holes are out of 
line may be minimised, but it cannot be eliminated by such means. 
The difficulty may sometimes be overcome by punching the holes 
smaller, and not reaming at all until the work is assembled ; but 
the canting of the reamer when only two thicknesses are to be 
reamed, with the holes in each out of line, must be prevented if such 
means are to be effective. 

If, owing to irregularity in shape, a hole be not completely filled 
by its rivet, some portions of the rivet will not be in contact with the 
metal in which the hole is formed, and hence no reliance can be 
placed upon the capacity of the rivet to transmit force from one 
piece to the other. In such cases, therefore, structural weakness 
may be inherent, as well as liability to leakage under the action of 
fluid pressure. 

Punching has for many years been believed to seriously damage 
the metal around the hole, and this was possibly the reason for 
insisting upon such holes being broached or reamed. Recent 
observation, however, appears to indicate that, given a sharp punch 
and a well-fitting nest, the damage is less serious, both in nature and 
extent, than was formerly supposed, and there is a tendency to 
punch holes more nearly the finished size, leaving only a small 
amount for reaming. This might have the advantage of slightly 
reducing the cost of reaming, but the difficulties due to holes being 
out of line would certainly not be lessened. 

7. Drilled Holes. — The introduction of high-speed tool steel for 
drills, and the improvements recently effected in electric driving 
for portable and other drilling machines, have done much to reduce 
the advantages in cost and time which punching formerly possessed 
over drilling for rivet-holes. In many of the best yards to-day, a 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING II 

large proportion of the rivet-holes are drilled, and although it is 
probable that punching will always be useful in some circumstances 
{e. g. for a few holes of medium size, through small thicknesses, as 
gusset plates and the like), drilling is wisely being adopted to an 
increasing extent. 

Less time is needed for marking and handling the work if the 
holes are to be drilled than if they are to be punched and reamed ; 
while, since each hole is formed in all thicknesses at one operation 
from a single marking, no difficulties can arise through holes being 
out of line. 

It is necessary to remove the burrs which the drill leaves on the 
surfaces as it emerges from each piece. This will be found requisite 
even though several pieces be drilled at one operation, each separate 
piece having a sharp rim around the hole, and unless these are all 
removed the pieces will not come together properly, nor will the 
rivets " cup-down " truly. Such burrs may be removed easily 
by running an old half-round file smartly along the row, knocking 
the burrs away. Similar burrs are, to some extent, formed also 
with punched-and-reamed holes. 

8. Nominal Rivet Diameters. — Owing to the fact that the 
diameter of the hole must be larger than that of the rivet as obtained 
from the makers, to permit the insertion of the rivet at a tem- 
perature suitable for closing, there is considerable diversity of 
opinion and practice as to whether the nominal diameter refers to 
the rivet as purchased or the hole. Some hold that the indication 
of (for instance) a f in. -diameter rivet on a drawing implies that the 
rivet-shank shall be | in. diameter when cold, and the hole ^^ in. 
or yV i^- larger; others work on the basis that the hole is | in. 
diamej;er, and the rivet (as purchased) slightly less. 

If the rivet, after driving, completely fill the hole, the latter 
method has the advantage in that the resistance of the rivet, and 
also the reduction in area of the pieces through which it passes 
(of importance when the pieces are in tension), may be properly 
calculated on the basis of a J in. -diameter rivet and hole; whereas 
the former method would give a rivet resistance greater, and a 
tensile resistance (of the pieces connected) less, than those calculated 
for a rivet and hole both | in. in diameter. On the other hand, if 
the finished rivet does not completely fill the hole, the former method 



12 



TANK CONSTRUCTION 



would appear to be preferable, since the rivet resistance would in 
most cases be lowered more by a reduction of ^V i^- i^ ^^^ diameter 
than would the tensile resistance of the pieces connected through 
an increase of yV i^- i^ the diameter of the hole. 

When each hole is drilled with all the pieces assembled (the drill 
being sent through all the pieces at one operation), and the rivets 
are properly driven by hydraulic pressure or pneumatic percussion 
machines, the holes are, in fact, completely filled, and hence, for 
such work, the nominal diameter may be the diameter of the hole. 

Endeavours are being made to bring about the adoption of a 
standard for practice in this matter ; and it appears probable that, 
at least for rivets driven by machine, the standard will be that 
the hole shall be of the stated diameter, and the rivet-shank as 
purchased only sufficiently less to permit of its insertion when hot. 



T'N^ 




»-o^o^ 



Fig. I. 



9. Proportions of Rivets. — Only snap and counter-sunk heads 
are now generally used for rivets in steel tank work. The proportions 
used by different makers vary slightly, but those given in Fig. i 
may be taken as representing good general practice. The dimensions 
of snap and countersunk rivet heads given in Table I. correspond to 

the proportions of Fig. i. 

TABLE I 
(All Dimensions in Inches) 



Diameter 


Snap. 


Countersunk. 


of 
Rivet 
















D. 


H. 


s. 


T. 


c 


1 


V. 


i 


1 3 

1 c 


i 


1 ff 


I 


-i\ 


I 


i 


i 


It% 


i 


Ii'^ 


1 


i 


If 


A. 


l| 


I 


ii 


i| 


i 


li 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 



13 



Some rivets are made with a portion of the shank sHghtly 
tapered, as in Fig. 2. Immediately under the head these rivets 
are almost the full diameter, so that the rivet fills the hole tightly. 
Two advantages are secured by this method— viz. (i) there is less 
space into which the rivet must be driven to secure a properly filled 
hole, and (2) the rivet is kept central in the hole while being closed. 

10. Yard and Field Riveting. — Practically all the yard riveting 
for tank work is done by hydraulic pressure or pneumatic percussion 
machines; only when no other means can be employed is hand- 
riveting used in the yard. The hydraulic pressure machine gives 
excellent results, and is much used for general steel- work; but 
it is less suitable for tank work because of the large distances to 
be spanned in many cases. In some yards where large tanks are 
made, yard riveting is limited to such items as fastening single 




Fig. 2. 

cover strips for butt joints to one plate, portions of framing which 
may conveniently be attached to the plates, and parts of the 
supporting or covering structural work; all other riveting being 
done at the site in course of erection. Such as these use hydraulic 
pressure machines for yard riveting, and either hand-riveting or 
pneumatic percussion machines at the site; but some prefer to 
use the latter method for all riveting, both in the yard and at 
the site. 

For " field " riveting {i. e. that which must be done during 
erection and fixing at the site), either hand or pneumatic tools 
are employed, according to the magnitude and importance of the 
work. A small job would not bear the cost, in ordinary circum- 
stances, of the plant necessary for pneumatic riveting ; but with an 
undertaking of considerable dimensions the cost of installing such 
plant at the outset would usually be more than repaid by the 
reduction in the cost of riveting, the saving in time and trouble, 



14 TANK CONSTRUCTION 

and the increase in the reUabihty of the work which would thus be 
obtained. 

The range of temperature in which steel can be worked is narrow, 
and therefore, unless the rivet can be placed in the hole immediately 
after its removal from the furnace, the temperature may fall below 
the allowable minimum, with the result that the material will not 
submit to the riveter as it should, even though great power be 
employed. Particularly is this the case with small rivets, in which 
the initial amount of heat is inevitably small. For this reason, 
some engineers prefer to use wrought-iron rivets for all field riveting, 
since they can be worked over a greater range of temperature 
without injury. The majority, however, specify steel rivets 
throughout, and insist upon the necessary care being taken to 
obtain good field riveting. 

Field rivets should never be more than | in. in diameter, and 
whenever practicable they should be limited to f in. diameter, 
owing to the difficulty of effectively working the relatively large 
amount of material by hand after the loss of heat during conveyance 
from the forge to the hole. This restriction is not so necessary in 
cases where pneumatic riveters are to be used at the site, and rapid 
transference of all rivets from the furnace to the hole can be ensured ; 
but even there it is a wise precaution to allow for unforeseen 
contingencies. 

II. Faults in Riveting. — If a rivet be burned or split, there will 
be little excuse for allowing it to pass. There are, however, other 
faults in riveted work which may escape notice in even the most 
rigorous examination, and which are almost impossible to remedy if 
discovered. Such should, therefore, be carefully guarded against. 

One of these faults is the formation of a rivet head not co-axial 
with the shank. It is more likely to occur in hand or pneumatic 
percussion work than with rivets closed by hydraulic pressure 
machine, as the frame of the latter is too strong and stiff to permit 
such twisting of its jaws as would be necessary ; it cannot happen 
with countersunk heads, of course, unless the rivet be too long. 
The most fruitful causes of this fault are : (i) Insufficient heat on 
the rivet; (2) excessive clearance in the hole — due either to small 
rivets or large holes ; and (3) carelessness on the part of the workmen 
and their supervisors. In the first and second of these causes the 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 1 5 

material prefers to bend over at the top rather than spread and 
flow, as it should, throughout its entire length. In the third cause 
it is less troublesome to simply turn the protruding point over than 
to drive the material carefully up into the clearance spaces, thus 
completely filling the hole first, and afterwards forming the snap 
so as to be truly concentric with the hole. 

Apart from the unsightly appearance of work in which this 
fault exists, there is obviously an element of weakness, both in the 
rivets and in the whole seam or member in which it occurs. All 
specifications for high-class work contain a clause to the effect that 
pieces in which the rivet heads are not well and truly formed, 
co-axial with the hole, will be liable to rejection. It would be 
useless to suggest cutting out the defective rivets as a remedy, for 
it is often impossible to say which heads are faulty and which are 
not ; the clause is therefore inserted as a lever, by means of which 
pressure may be brought to bear which will ensure the exercise of 
due care in this respect. 

A point in connection with countersunk heads is worthy of 
notice. Some engineers insist on the surface being chipped level 
after riveting, while others prohibit such chipping on the ground 
that " it makes the rivets loose." Now, while it often happens 
that a countersunk rivet which appeared to be tight when driven 
is found to be slack after chipping, it does not follow that the 
chipping has caused the slackness ; it is more likely to have simply 
revealed it. Instead of upsetting properly and filling the hole, 
the material sometimes (especially if the rivet^be too long) spreads 
over the counter-sinking sufficiently to take all the pressure, and it 
is this rim which holds the rivet (apparently) tight. As soon as the 
projecting layer is chipped away, the slackness of the rivet is made 
known ; and the worst of it is that, until it has been chipped, it is 
impossible to say whether such a rivet is tight or not. 

12. Lengths of Rivets for Ordering.- — ^The length of shank which 
should be allowed beyond the " grip " — i. e. the total thickness 
of the pieces to be connected — for filling the hole and forming the 
head depends upon the style of work {i. e. whether hand or machine), 
and also upon the rivet diameter and grip, since the hole space 
to be filled varies directly with the size and length of the hole. 
If the rivet be too short, there will not be sufficient material to 



1 6 TANK CONSTRUCTION 

properly form the head after fiUing the hole ; and if too long, a rim 
will be formed round the head, which may prevent the tight driving 
of the rivet, in a manner similar to that described above in connection 
with the countersunk head. 

When ordering rivets from the manufacturers it is necessary 
to state the diameter, length under head to point, and type of head 
required. Particular care is necessary, in stating the diameter, 
to prevent the possibility of misunderstanding between actual 
and nominal diameters as explained above : if the holes are larger 
than the stated size, the rivet shank should be of the full stated 
diameter; and if the holes are the actual net diameter stated, the 
rivet shank should be some less diameter. In the former case a 
conspicuous note should be placed on the order to the effect that the 
rivets are to be of the actual diameters stated in the order, and 
in the latter case an equally conspicuous direction that the rivets 
are to be of diameters suitable for holes of the diameter stated. 
Perhaps the best method is to state the exact diameter of rivet 
shank required in every case for all orders, and the note may then 
be printed prominently on all order forms. The length to be 
stated is that represented as L in Fig. 2 (p. 13). 

Lengths of rivets for ordering, for grips likely to occur in tank 
work, are given in Table IL These lengths have been found to give 
good results in practice, for hand and machine (hydraulic or pneu- 
matic) riveted work. 

Thus, a j in. -diameter rivet to secure three J in. plates, to be 
driven by machine, and to have snap head and point, would require 
to be 2-| in. long under head to point. A rivet of the same diameter 
and grip, to be hand-driven, should be J in. less in length — i. e. it 
should be ordered 2| in. long. 

13. Rivet Diameters. — The determination of the diameter of the 
rivets to be used in a piece of work, if the best results are to be 
obtained, is not alwaj^s so simple a matter as is sometimes supposed. 
There are, of course, first the questions of strength and tightness, 
and the necessary diameter of the rivets may be calculated by 
simple arithmetic after adopting, more or less arbitrarily, some 
particular disposal or arrangement of the rivets; but there are 
other considerations which should be taken into account before 
accepting the size so found. Regard should be paid to economy 



MATERIALS,, PERMISSIBLE STRESSES AND RIVETING 



17 



TABLE II 
Lengths of Rivets for Ordering, in Inche- 



Grip 
in 






Diameter of Rivet, in Inches. 








Snap Head. 






Countersunk. 




In. 




















1 


If 


1 


I 
2 


li 


1 


1 
li 


i 
If 


I 


i 


If 


i| 


li 


if 


i 


If 


If 


i| 


2 


2i 


li 


If 


if 


li 


14 


3 

X 


If 


li 


2 


2i 


2i 


If 


li 


li 


If 


If 


1 


i| 


2 


2i 


2i 


^8 


li 


if 


If 


il- 


If 


I 


2 


2i 


2i 


2| 


2i 


If 


I| 


If 


i| 


i| 


li 


2i 


2i 


2| 


2i 


2| 


if 


I| 


i| 


2 


2 


li 


2i 


2-1 


2i 


2| 


2f 


i| 


2 


2 


2i 


2i 


if 


2| 


2i 


2f 


2i 


2| 


2 


2f 


2f 


2i 


2| 


u 


2i 


2f 


2| 


3 


3i 


2i 


2i 


2i 


2f 


2i 


ll 


2f 


28 


3 


3i 


3i 


2i 


2f 


2j 


2j 


2f 


If 


2f 


3 


3i 


3i 


31 


2| 


2i 


2f 


2f 


2| 


II 


2| 


3i 


3i 


3f 


02 


^2 


2f 


2| 


2f 


2| 


2 


3 


3l 


3h 


3f 


3f 


2f 


2| 


7 

2^ 


2| 


3 


H 


3i 


3i 


3f 


3i 


3l 


2i 


2| 


3 


3 


3i 


2i 




3f 


3l 


3l 


4 


— 


3 


3i 


3i 


3i 


2| 


— 


3l 


3l 


4 


4i 


— 


3f 


3i 


3i 


3f 


2i 


— 


3l 


4 


4i 


4i 


— 


3i 


3f 


3f 


3i 


2f 


• — 


4 


4i 


4i 


4l 


— 


3f 


3i 


3i 


3f 


2| 


— 




4i 


4l 


4i 


— 


— 


3f 


3f 


3l 


2f 


— 


— 


4l 


4i 


4f 


— 


— 


3l 


3l 


3l 


3 


— 


— 


4i 


4f 


4l 





— 


3l 


4 


4 


3i 


— 


— 


4f 


4f 


4i 


— • 


— 


4 


4i 


4i 


3i- 


— 


— 


— 


4I 


5 


— 


— 


— 


4i 


4f 


3f 


• — 


— 


— 


5 


5i 


— 


— 


— 


4l 


4i 


3^ 


— 


— ■ 


■ — 


5i 


5i 


— 


— 


— 


4i 


4f 


3f 


— 


— 


— 


5i 


5l 


— 


— 


— 


4f 


4l 


3i 

3l 
4 


— 


— 






5i 
5f 
51 ' 




— 


— 




4l 
5i 
5i 


4i 
4i 
4I 




— 


■ 


— 


5l 
6 

6i 




■ — 


— 


— 


5f 
5i 
5f 


4i 




' 




■■ 


6| 










— 


5l 



The above lengths are for machine riveting, 
should be reduced by J in. 



For hand riveting the lengths 



of labour, material, and weight; a proper relation should exist 

between the diameter of the rivet and the total thickness of the 

pieces through which it passes ; and facility (and, therefore, economy 
c 



i8 



TANK CONSTRUCTION 



of labour) in driving the rivets should be secured. Each of these 
matters has a direct and important bearing on the proper diameter 
of the rivet to be used. 

It has been found that a tight rivet and well-filled hole cannot 
be assured if the grip exceeds four times the diameter. A f in.- 
diameter rivet should, therefore, not be used if the total thickness 
of the pieces through which it would pass exceeds 2 J in. ; the grip 
of a I in. -diameter rivet should not be more than 3 in., and so on. 
Further, since the total cost of riveting is more nearly proportional 
to the number of rivets used than to their diam.eter, it is clearly 
more economical to use a small number of large rivets than a large 
number of small rivets, though this latter consideration may some- 
times be outweighed by requirements for tightness against leakage, 
and other circumstances. 





Fig. 3. 



For facility in riveting it is necessary that adequate clearances 
be provided for the dies or tools, either hand or machine, both for 
closing and holding up the rivet. Two typical cases in which such 
clearances must be provided are indicated in Fig. 3. The distance 
C in each case should be not less than JS + y V ^^-^ ^ being as given 
in Table I. Difficulties in this direction may sometimes be lessened 
by judicious zig-zag spacing. It is better to allow for a slightly 
greater height of head than as given in Table I., as the rivets do not 
always close perfectly; the extra allowance should be yV iri. for 
rivets up to f in. diameter, and J in. for the larger sizes. This 
determines the largest diameter of rivets which may be used with 
any angle, tee, channel, joist, or other rolled section, for any 
particular arrangement of pitch-lines. 

The diameter may also be affected by limitations of pitch, etc.. 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING IC) 

but the rivet finally selected should be of such diameter as will 
give the best agreement obtainable with all the foregoing require- 
ments. 

14. Pitch and Arrangements of Rivets. — In tank work the majority 
of joints and seams are single-riveted, and either lap-joints or butt- 
joints with double cover strips. Occasionally, where fluid pressures 
are great, double or treble riveted joints may be necessary, and the 
rivets are then " staggered "• — i. e. arranged zig-zag — so that the 
sectional area of the pieces connected may be reduced as little as 
possible at any particular cross-section. 

The pitch, for tightness of the joints against leakage, is almost 
invariably taken as three times the diameter of the rivets ; but, 
while it should not be less than this, it may be slightly more where 
necessary, to keep a uniform pitch along a seam — e. g. w^hen a 
pitch of three times the rivet diameter is not contained an integral 
number of times in the total length of the seam. No considerable 
increase of pitch should be permitted, however, unless the plates 
are stouter than is necessary for strength requirements, and will 
therefore work at a lower stress than would otherwise be allowed ; 
and even then a pitch more than three-and-a-half or four times the 
(iiameter of the rivets is likely to cause trouble through " weeping " 
and the consequent corrosion. 

Adequate provision must be made to prevent tearing of the 
plates beyond the rivets, and for this purpose the centre of a rivet 
should be at least one-and-a-half times the diameter of the rivet 
from the edge of any plate or bar through which it passes. Where 
the edge of the plate is not planed, and if the joint be important or 
heavily loaded, the distance between the centres of the rivets and 
the edges of the plates should be not less than twice the diameter 
of the rivets. 

Other points regarding the most suitable arrangement for 
rivets, and the form of joint which should be adopted, in particular 
circumstances, will be indicated and discussed when considering 
the design of the various types of tanks. 

15. Rivet Resistances. — ^The resistances of rivets to shearing 
and crushing (i. e. in bearing) are calculated on the nominal diameter, 
for the permissible stresses of 5*5 tons per sq. in. in shear, and 11 tons 
per sq. in. in bearing, except that the resistance of a rivet in double 



20 



TANK CONSTRUCTION 



shear is usually taken as 175 times the resistance of the same rivet 
in single shear. Experiments have indicated (and the more favour- 
able loading of the rivet would lead to the assumption) that a rivet 
in double shear may carry twice the load which would be borne 
by the same rivet in single shear, but the Board of Trade, and other 
authorities, permit a load on a rivet in double shear of only 175 
times the load allowed for a rivet of the same diameter in single 
shear — hence, all riveting in structures requiring the sanction or 
approval of such authorities must be designed accordingly. In 
work not requiring such approval, the resistance of a rivet in double 
shear is often taken as twice that of the same rivet in single shear, 
and it is probable that no great harm is thereby done. 

Bearing resistances are calculated on the " projected area " 
of the actual bearing; thus, in a lap joint the bearing area would 
be taken as the projected area of the rivet in one plate thickness 
only. 

Permissible shearing and bearing resistances of rivets, in single 
and double shear, and for various thicknesses of bearing, are given 
in Table III, double shear being taken as equivalent to 175 times 
single shear. 

TABLE III 



RESISTANCES OF MILD STEEL RIVETS 



Di- 
ameter 
1 of 
; Rivet 


Cross- 
sectional 
Area in 

sq. in. 

0-1963 
0-3068 
0-4418 
0-6013 
0-7854 


Shearing Re- 
sistances in 
tons, at 5-5 
tons per sq. in. 


Bearing Resistances in tons, at ii tons per sq. in. 


Thickness of actual bearing, in inches. 


in 


Single 
Shear. 

I -08 
1-69 
2-43 
3-31 
4-32 


Double 
Shear. 


inches. 


i 
1-38 

1-72 


^ 


f 


is 
2-41 

^•01 


i 

2-75 


t\ 


3-44 
4-30 
5-i6 

6-02 


n 

4-73 
5-67 
6-62 


t 
6-19 

7-22 
8-25 


U 

7-82 
8-94 


i 


1 

i 

i 

I 


1-89 
2-95 
4-25 
5-79 
7-56 


1-72 1 


2-o6 


3-09 


9-63 


2-15 

3-OI 1 
3-44 


2-58 
3-09 

4-13 


3-44 


i-87 

5-41 
6-19 


2-o6 

2-41 

2-75 


3-61 

4-21 1 
4-81 j 


4-13 1 
4-8i 

5-50 


6-88 


7-56 



Bearing resistances above the upper heavy stepped line are more 
than the resistances in double shear; hence, in these cases, shear 
is the determining factor. Bearing resistances between the heavy 
stepped lines are more than single shear and less than double shear ; 
hence, the determining factor in these cases will be shearing for 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 21 

single shear, and bearing for double shear. Bearing resistances 
below the lower heavy stepped line are less than the resistances in 
single shear; hence, in these cases, bearing is the determining 
factor. 

It should be noticed that shearing resistances vary with the 
square of the rivet-diameter, the length being ignored, while bearing 
resistances vary as the product of the diameter and length of actual 
bearing ; moreover, the stress allowed for bearing is twice that for 
shear. Hence, there may be considerable difference between 
the resistance of a particular rivet to shear, and the resistance of 
the same rivet to crushing, by reason of the relation borne by the 
plate-thickness to the rivet-diameter. Obviously, only the smaller 
of these two resistances may be taken as the resistance of the rivet, 
and loss of economy may arise in consequence. Where practicable, 
endeavours should be made so to design the riveting that all resist- 
ances shall be as nearly equal as may be, thus avoiding waste of 
material or labour. 

For rapid checking, and in cases where an approximate estimate 

only is needed, it is convenient to memorise the shearing resistances 

of rivets as follows : J in. diameter, i ton single shear, 2 tons double 

shear ; f in. diameter, 1*5 ton single, 3 tons double ; f in. diameter, 

2 "25 tons single, 4*5 tons double ; | in. diameter, 3 tons single, 6 tons 

double; and i in. diameter, 4 tons single, 8 tons double. These 

are round figures, easily remembered, and, as will be seen, not much 

in error. Bearing resistances may be easily calculated by the 

following simple relation — 

-p (/g X Cig), 

K, - g 

where R^ is the resistance (bearing), in tons, and t^ and dg are the 
plate-thickness (actual bearing) and rivet-diameter respectively, 
both expressed in eighths of an inch. Thus, for example, with a 
I in.-dia'hieter rivet bearing in a f in. plate, t^ and d^, expressed in 
eighths of an inch, would be 6 and 5 respectively, and hence the 

bearing resistance of the rivet would be : R^ — ^^ — ^— ^ = 5 tons, 

which is very nearly correct, while the process is suitable for 
operation mentally. It is much easier to use than to describe. 
In passing, it should be observed that the desirability of securing 



22 TANK CONSTRUCTION 

(approximately) equal resistances to the various straining actions 
in a seam, constitutes another factor in the selection of the most 
suitable diameter for the rivets in any particular instance, to be 
taken into account simultaneously with the other considerations 
already mentioned in pp. 16-19. 

16. Friction in Riveted Joints. — There is one fact concerning 
riveted joints which, though of real importance, is seldom men- 
tioned — viz. that there is friction between the pieces through which 
the rivets pass. Having regard to the roughness of the surfaces 
of commercial steel plates and bars, and the considerable amount 
of tension set up in the rivets during cooling, there must be large 
frictional resistances to relative motion of the pieces, altogether 
apart from the rivet-resistances. Any proposal to estimate the 
magnitude of such frictional resistances would probably be regarded 
as unpractical, and calculations relating thereto would certainly 
be discounted by the opposing fact that both the roughness of the 
surfaces and the tension in the rivets are variable and practically 
indeterminate ; but, on the other hand, it would be absurd to deny 
their existence. 

Clearly, if it were possible to secure sufficient frictional effects 
by other means, rivets would become unnecessary, and this fact 
has recently been made use of in the construction of small vessels 
of a nature similar to tanks, when, owing to the difficulty and cost 
of obtaining good riveted work, the seams were welded by means 
of one of the new processes. In the ordinary way, of course, it is 
doubtful whether sufficient surface friction (i. e. between surfaces 
pressed together, but not welded) could be developed even for mere 
strength purposes, and it is probable that no scam could be made, 
tight against fluid pressure by such means ; but friction between 
the pieces connected must, beyond question, relieve the rivets to 
some extent in their resistance to shearing and crushing, and also 
tend to produce a more uniform distribution of stress over the 
pieces connected than would be the case were the rivets and plate- 
surfaces quite frictionless, as is assumed in calculations. At least 
it would appear that these facts might be taken into account where 
the calculated stresses in the rivets of a seam are slightly (say 4 or 
5 per cent., as not infrequently happens) in excess of the agreed 
permissible stresses, especially if there be a good number of rivets 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 23 

in the seam, for each rivet will assist in producing friction between 
the surfaces. 

17. Weight of Tankwork. — The weight of tankwork is estimated 
on the basis that a cubic foot of steel weighs 489*6 lb. Other con- 
venient figures, derived from this, are that a square foot of steel, 
one inch in thickness, weighs 40 "8 lb., and a foot run of one inch 
square steel bar weighs 3*4 lb. 

A cubic foot of wrought iron weighs 480 lb., so that a square foot 
of wrought iron, one inch in thickness, weighs 40 lb. 

Cast iron weighs 454*5 lb. per cub. ft., and for weight calculations 
one cubic inch may be taken as weighing 0*263 lb. 

All standard rolled steel sections have a definite weight per foot 
run, and joists, channels, angles, etc., should be ordered and 
calculated by their listed weights as well as by their over-all cross- 
sectional dimensions. 

Approximate weights of rivets, as purchased from the manu- 
facturers, are given in Table IV, and the various allowances at 
the foot of each column render the table applicable to rivets of any 
length, and with either snap or countersunk heads. It is useful 
for checking the number of rivets in a bag without counting, and 
also for estimates, etc., for the purposes of shipment and carriage. 

In calculating the weight of riveted work it is only necessary to 
allow extra for the heads of the rivets, the shanks being accounted 
for by considering all plates, bars, etc., as solid. The usual practice 
is to count the heads, and multiply the number of them by the 
weight of one head, given at the foot of Table IV. It is necessary 
to note that each rivet has two heads. 

Another method- — which is, perhaps, slightly quicker, and which 
has the advantage of being independent of tables — is to count the 
number of heads, and consider each snap as the piece of shank from 
which it was formed; that is to say, take each head as a piece of 
round «rod, of the same diameter as the rivet, and of length equal 
to one-and-a-half times its diameter. This is not strictly correct 
for rivets over | in. diameter (being slightly excessive), but 
since such large rivets are seldom used, the rule may be followed 
with confidence for all ordinary work. 

No allowance need be made for countersunk heads, of course. 

The practice of estimating " by eye " the weight of rivet heads 



TABLE IV— STEEL SNAP-HEADED RIVETS 
Weight in Pounds per too 







Diameter in Inche 


s. 




Length under Head 
to Point in Inches. 












i 


f 


i 


i 


I 


If 


II-8 














H 


12-5 


21-2 


32-8 


— 


— 


i^ 


13-2 


22*3 


34-4 


50-0 


69-5 


If 


1 3 '9 


23-4 


36-0 


52-2 


72-3 


i| 


14-6 


24-5 


37'6 


54'3 


75-1 


2 


15-3 


25-6 


39-1 


56-4 


77'9 


2i 


i6-o 


26-6 


407 


58-6 


807 


H 


16-7 


27-7 


42-2 


60-7 


83-4 


2| 


I7'4 


28-8 


43-8 


62-8' 


86-2 


2h 


i8-i 


29-9 


45*4 


• 64-9 


89-0 


2{ 


i8-8 


31-0 


46-9 


67-1 


91-8 


2f 


19-5 


32 'O 


48-5 


69*2 


94 '6 


2i 


20-2 


33-1 


50-1 


71-3 


97'4 


3 


20"9 


34-2 


51-6 


73-5 


lOO'I 


3^ 


21-6 


35-3 


53'2 


75-6 


102*9 


3k 


22*3 


36-4 


54-8 


777 


1057 


3l 


■ 


37-5 


56-3 


79-8 


108-5 


3^ 


■ — • 


38-6 


57'9 


82-0 


III-3 


3l 





39-7 


59-5 


84-1 


114-0 


3l 





407 


61 "O 


86-2 


116-8 


3i 





41-8 


62-6 


88-4 


119-6 


4 





42-9 


64-2 


90-5 


122-4 


4^ 





— 


65-7 


92-6 


125-2 


4.i 





— 


67-3 


947 


127-9 


4l 


■ 


— 


68-8 


96-9 


130-7 


4i 





— 


70-4 


99-0 


133-5 


4l 


— 


— 


72*0 


loi-i 


136-3 


4* 


--- 


— 


— 


103-3 


139-1 


4t 





— 


— 


i05"4 


141-9 


5 




— 


— 


107-5 


144-7 


5i 





— 


— 


1097 


147-4 


5i 





— 


— 


III-8 


150-2 


5| 


- — 


— 


— 


— 


153-0 


5^ 


— 


— 


— 


— 


155-8 


5f 





— 


— 


— 


158-5 


5l 





— 


— 


— 


161-3 


5^- , 





— 


— 


— 


164-1 


6 





— 


— 


— 


166-9 


61 


' 





— 


— 


169-7 


61 





— 


— 


— 


172-5 


6f 





— 


— 


— 


175-3 


Weie[htof Toosnnp' 












heads . 


4-2 


8-2 


14-1 


22-4 


33-4 


Weight of loo 












■countersunk heads 


3-5 


5*4 


9-4 


15-0 


22-3 


Weight per inch ot 












shank, per loo . 


5-6 


• S'7 


12-5 


17-0 


22*3 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 25 

in a piece of work, and expressing it as a percentage of the weight 
of the plates and bars making up the piece, is very convenient for 
those whose experience has been wide enough to enable them to 
judge what would be a fair allowance for any particular case ; but 
as these allowances may vary between comparatively wide limits 
in different classes of work, considerable error may be caused by 
a slight lack of discernment. Unless the result is only required to 
be a rough approximation, it is always best to determine the actual 
number of heads, and calculate their weight by one of the methods 
explained above. 

i8. — Permissible Stresses. — With mild steel plates and bars of 
British Standard Specification it is usual to calculate plate-thick- 
nesses upon the basis of permissible stresses not exceeding — 

7*5 tons per sq. in. in tension ; 

7*5 ,, ,, in compression (pure, and in bending — not for stanchions 

and struts) ; 
5' 5 ,, ,, in shear; and 

II ,, ,, in crushing (or bearing). 

For rivets, as has already been stated, the maximum permissible 
stresses are generally taken as 5*5 tons per sq. in. in shear, and 
II tons per sq. in. in bearing. 

These represent good ordinary practice, and may be regarded 
as a basis from which modifications may start in exceptional circum- 
stances, where either, on the one hand, a relaxation of the standard 
is reasonably permissible, or, on the other, greater stringency is 
required. 

It is sometimes argued that, since the loading in tankwork is 
not subject to large or rapid fluctuation, higher stresses may be 
allowed, both in plates and rivets. Instances do occur, as suggested 
above, where conditions are very favourable, and advantage may 
(and should) then be taken of the circumstances to secure the utmost 
economy of material. Such instances are, however, exceptional, 
and should be so regarded. To design for stresses appreciably 
greater than those stated above, in ordinary circumstances, is 
unjustifiable and improper, as will be seen presently. 

The maximum permissible stresses to be used as a basis for 
design depend upon several factors, mostly independent of each 
other. The more potent of these factors may be classified under 
five broad headings, thus : (i) The physical properties of the 



26 TANK CONSTRUCTION 

materials ; (2) the effects of processes of manufacture and handling 
upon the materials; (3) the nature and circumstances of loading; 
(4) the conditions under which the materials will work, and the 
permanence required; and (5) the so-called "factor of safety." 
As these matters, though of the greatest importance, are by no 
means well understood, we will consider them separately and in 
some detail, so that their influence upon practical tank structures 
may be properly appreciated. It is only by means of a clear under- 
standing of the facts, and logical reasoning therefrom, that true 
economy can be obtained; and the flippant haziness with which 
the problems of the design and construction of tanks are so often 
treated results in much waste that could easily be avoided or 
counteracted. 

(i) Physical Properties of Materials. — All structural design is 
based upon the assumption that the materials are elastic, and with 
mild steel this assumption is reasonably justified over a certain 
limited range of stresses. Beyond that range, however, the material 
becomes, to a considerable extent, plastic, and no basis for design 
under such conditions is practicable. For the purpose of designing 
commercial structures, the stress at which the material ceases to 
be elastic should be regarded as the ultimate strength, and in mild 
steel this stress is about one-half of that under which the material 
would actually break in tension. 

If a part of a structure be strained beyond the elastic limit — 
i. e. beyond its power of recovery on removal of the load, — many 
things may happen, but it is not necessary either to discuss or to 
enumerate them here ; nor is it necessary to differentiate precisely 
between " elastic limit " and '' yield point." It is sufficient to 
notice that in a tank something much less spectacular than the 
actual breaking of a plate or piece may be sufficient to cause serious 
damage ; with plates or rivets which have been stressed to such an 
extent that they are no longer elastic, it is evident that the tightness 
of the seams cannot be assured, and when that stage is reached the 
utility of a tank has practically been destroyed. 

Moreover, ordinary calculations take account of primary stresses 
only, and assume either uniform distribution or uniform variation 
of stress over the whole section. There are, as a fact, always 
secondary stresses, some of which would be almost impossible to 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 



27 



estimate, but which are known to be highly important. By taking 
the permissible working stresses as stated above, therefore, and 
ignoring the secondary stresses, we are really only allowing a similar 
amount for the sum of all the secondary stresses — due to inequalities 
in the materials, and other defects, which are not taken into account 
in the calculations, but which exist none the less for that. 

(2) Effects of Manufacture. — It is well known that commercial 
rolled steel bars are not perfectly straight, nor of constant cross- 
section, nor can they be made so. Steel plates, again, as bought 
from the mills, are neither flat nor of uniform thickness throughout. 
During transport, pieces 

often become so further T^ZT^r-^r^,., ^_ 

bent that they have to ^ ""^ '^ ^ ^ . . 

be again straightened 
before the processes of 
manufacture can pro- 
ceed, and since such 
straightening is nearly 
always done without 
heating the material, 
parts must inevitably 
be strained beyond the 
elastic limit. Among the 
operations which are 
performed during manufacture, several cannot fail to set up initial 
stresses in the pieces connected, and the final result is that a member 
which has a calculated primary stress of 7*5 tons per sq. in. may be 
really subjected, at least in parts, to considerably more. 

\\'ith some sections — angles and channels in particular — rivets 
cannot be driven so that their axes will lie in a plane which contains 
the centre-of-gravity line of the section, and consequently forces 
applied to a bar through such rivets are unavoidably eccentric, 
causing bending actions. As an example of what may occur, 
consider the case illustrated in Fig. 4, the angle bar acting as a tie. 
The primary stress, on the assumption that the direct tensile load 
is distributed uniformly over the net section, is about 3 tons per 
sq. in. ; but there is also a bending moment of somewhere about 
2 in. -tons with regard to both axes, and since the section modulus 




Fig. 4. 



28 



TANK CONSTRUCTION 




^^^^ 



^^^ 



about those axes is about 0*38 (inch units), the stress due to the 
bending action, to a first approximation, will be about 5 or 6 tons 
per sq. in. In addition there may be stresses due to the bending 
action caused by the weight of the bar if its axis be not vertical. 

Stiffness and friction in the joints unquestionably reduce these 
stresses, but cannot eliminate them, and there are also other stresses 
due to irregularities in shape and inequalities in the material, which 
can only be guessed in any particular case. 

In riveted seams, with the lap joint and single-covered butt 
joint connecting two pieces in tension, there is the well-known 
tendency to distortion as indicated in Fig. 5, and this must set 

up considerable additional stresses in 
the plates as well as in the rivets. 

These and many other effects which 
cannot be prevented or calculated 
accurately, must be to a reasonable 
extent provided for. It has been 
estimated that in some classes of struc- 
tural steelwork the secondary stresses 
together are not less than the primary 
stresses, and while they are probably 
not so severe as that in tank work, there can be no doubt that 
they form a considerable part of the total stresses. 

(3) Conditions of Loading. — Alternating and fluctuating loads 
cause more stresses than do steady loads of equal magnitudes. 
The loads in tank work are usually steady, but this fact cannot of 
itself be a sufficient reason for allowing higher stresses, because it 
is generally agreed that when varying loads have to be provided for, 
the permissible stresses should be reduced according to the range 
of variation. 

There are instances, as will be seen later, where advantage may 
be taken of the circumstances of the stresses in adjacent material, 
to avoid using a thicker plate when the calculated stress is in excess 
of the maximum permissible by only a small percentage, but other- 
wise there is no justification in the steadiness of loading for raising 
the limits of working stresses. 

In one way, the parts of a tank are less favourably placed than 
those of some other structures. In the latter it often happens that 




Fig. 5. 



MATERIALS, PERMISSIBLE STRESSES AND RIVETING 29 

a member which receives more than its due load can, by distorting- 
slightly, obtain assistance from other members or construction. 
No relief can be found in a tank, however, except by reducing the 
pressure of the contained liquid, and this is usually prevented by 
some device for maintaining the level as nearly constant as may be. 

(4) Conditions of Working and Fermanence. — With a tank con- 
taining water which is not very frequently changed, there is usually 
little or no corrosion, and if the exterior surfaces be ordinarily well 
protected, the tank may be designed for the working stresses stated 
above. When a tank is liable to be emptied and filled in rapid 
and continual sequence, some allowance should be made for corro- 
sion, which will then be more effective than with water which is 
merely stored. 

It is usual to provide such allowance for corrosion by lowering 
the maximum permissible stress to 7 or 6'5 tons per sq. in., which, 
of course, has the effect of slightly increasing the thickness or other 
dimensions of the sections. It is difhcult to justify this means, for, 
clearly, there can be no connection in fact between the working 
stress and the provision necessary on account of corrosion, and no 
distinction is made by it between pieces which have only one surface 
and those which have more exposed to corrosive action. Moreover, 
it does not provide equally on all sections, though the action of 
corrosion cannot so vary from point to point. 

A more logical method is to design for thickness on the above 
basis of working stresses, and then to increase the thickness so 
obtained by some definite amount, say, ^V in. or ^^ in., as experience 
indicates. If a piece were, by some means, found to be stressed 
(by primary calculation) below the maximum permissible, the net 
thickness required might be determined, and if the actual thickness 
provided a sufficient margin for corrosion nothing further need 
be added. 

As is well known, corrosion due to water is more active in parts 
altegiately wet and dry than in parts wholly wet or dry, and hence 
care should be taken to provide adequately over the range between 
high and low water levels. 

If the tank is to contain some liquid which attacks steel with 
chemical action, data as to the rate of decomposition will be neces- 
sary, and provision should be made by additional thickness calcu- 



30 TANK CONSTRUCTION 

lated according to the length of time the tank is required to last. 
In such cases, of course, frequent examination is necessary, so that 
local inroads — about cracks in seams, rivet heads, and similar places 
— may be detected and arrested. 

Some tanks are continually subjected to the action of fumes — 
frequently of sulphur, as at railway depots; and here, again, the 
allowance for corrosion should be based on experience as to the rate 
of attack, and the degree of permanence required. 

All such allowances should be liberal rather than the reverse, 
and based upon some reasonable estimate. 

(5) Factor of Safety. — This is more properly a " margin for 
contingencies." As a similar instance, on a railway platform one 
might say that, for safety when an express train is passing or 
approaching, one should not be less than 7 ft. from the edge. This 
would allow a margin of 7 ft. to provide for suction, possible pro- 
jections from the train, involuntary movement, and such things, 
which experience has shown should be provided for. A platform 
14 ft. in width might then be said to give a " factor of safety " of 
2, but the essential fact is that a margin of 7 ft. is required, irrespec- 
tive of the platform width beyond that margin. 

If it were known positively that the train would pass at a low 
speed, that there would be no projections from it, and that no 
involuntary movement of any magnitude could occur, a distance 
less than 7 ft. could safely be allowed. In the case of mild-steel 
■structures, the working stresses stated above leave a margin of 
about the same magnitude for secondary stresses, inequalities in 
the material, etc., and usually this is found to give satisfactory 
results. Sometimes (as when secondary stresses are known to be 
highly effective) a wider margin should be allowed ; and sometimes 
a less margin will be sufficient. 

One frequently hears arguments in favour of high working 
stresses based upon the shortness of life intended for the structure. 
Of course, if it could be ensured that the structure would be de- 
molished at the end of a certain period, allowances for corrosion 
and similar effects might reasonably be made for that period only, 
but the intensity of pressure due to a certain head of water is not 
less if exerted for one year than if exerted for twenty years, and any 
considerable increase of permissible stresses on this account is 



MATERIALS, TERMISSIBLE STRESSES AND RIVETING 



31 






unjustifiable. The utmost that might be allowed would be to so 
design the parts that, by the end of the term stated, the total 
stresses from all causes would be in the neighbourhood of (but not 
likely to exceed) the elastic limit. Even this, however, is ver}^ 
seldom warrantable. 

Moreover, structures (and tanks particularly) which are regarded 
as temporary when erected, have a knack of becoming very soon 
afterwards regarded as permanent, and it is difficult, if not im- 
possible, to form a reliable estimate of the period during which they 
are likely to be retained. 

The only circumstances in which the maximum permissible 
stresses stated above may be increased, are such as permit a reason- 
ably exact computation of all the stresses,- — secondary as well as 
primary, — or the strong probability 
that they will not exceed a certain 
amount. Then the margin between 
the total of all the stresses and that 
stress which marks the limit of 
elasticity might be only two or three 
tons per sq. in. Such cases seldom 
arise, however, and it is generally 
better to follow the course which 
experience has shown to be satis- 
factory, adopting the limits of working stresses given above, and, 
as a rule, ignoring secondary stresses. 

19. — Caulking. — No jointing material should be permitted in 
the riveted seams of tanks. All the necessary tightness against 
leakage may be obtained by caulking the plate edges, as indicated 
in Fig. 6. Caulking may be done by hand or by pneumatic machine, 
but the latter is rather apt to cause damage to the plates, owing to 
the difficulty of controlling the tool while being operated at a high 
speed. The tool should be rounded on the edge which bears upon 
the lower plate, as shown, to avoid cutting into that plate. Some 
authorities state that the caulking edges of the plates should be 
planed with a bevel, the angle being about 80°, as indicated in 
Fig. 6 ; but this is seldonc done. Many caulk only the inner edges 
of the seams, where exposed to the contained liquid, leaving those 
outside the tank as riveted. This should be done with sufficient 




32 TANK CONSTRUCTION 

thoroughness to prevent leakage, of course, for any Uquid finding 
its way into the joint will probably cause trouble ; but it is better 
to caulk all edges, so that moisture from the atmosphere and weather 
may not enter and set up corrosion where it would be difficult to 
see or check. 

Butt joints have more edges to caulk than lap joints, but, being 
stiffer, the caulking is both less troublesome to do and more likely 
to be effective. 



CHAPTER II 

ECONOMY OF FORM 

20. — Economy of Form. — The obvious and primary measure of 
the utihty of a tank is its capacity for storage, while its cost, as a 
tank, is the cost of the shell. In many cases, of course, the tank 
must be carried upon some sub-structure (elevation being necessary, 
as well as capacity), and the cost of the sub-structure may be more 
than that of the tank itself, while it is often advisable to sacrifice 
economy in the tank so that a higher degree of economy may be 
obtained in the structure as a whole. These points will be illus- 
trated later, but for the moment it is well to consider the tank 
by itself. 

Now it might appear (and, indeed, has sometimes been stated) 
that the most economical form for a tank must be that which gives 
the greatest cubical contents for the least area of containing shell. 
This, however, ignores the very important fact that the cost is 
not always directly proportional to the area of the plating. The 
saving in area may be counterbalanced (or, at least, partly so) by 
a greater thickness of plate being rendered necessary in conse- 
quence, or the need for auxiliary stiffening, owing to the increased 
pressures of the contained liquid brought about by the particular 
form of the tank. Moreover, even with the same thickness of 
plate, the cost of a small area in a class of work involving much 
labour may be more than that of a larger area in simple work. 

Thus, it will be seen that to claim that one form is more econo- 
mical jthan another solely because the one requires a little less weight 
of material than the other, may be unjustifiable unless saving in 
weight be more important than any other consideration. It does 
happen, sometimes, that, by reason of the special circumstances 
and conditions, a saving in one particular respect is more desirable 
than a greater saving either in other respects or in general, but as 
D 33 



34 TANK CONSTRUCTION 

a rule, the economy to be sought is that which includes all aspects 
and secures the best return for the least outlay. 

The foregoing remarks are not intended to imply that the form 
which gives .the minimum area of sheeting for a specified volume 
is of no practical use, and may therefore be ignored; on the con- 
trary, unless the particular circumstances of the case require that 
a certain form shall be used, that which gives the least area of 
sheeting should be determined, so that it may be seen whether it 
will give, or may be modified to give, the most economical design. 

In comparing the suitability and efficiency, for tank work, of 
flat plates with those of plates bent to some curved shape, it should 
be noted that a flat plate must act as a beam, and hence, that only 
the equivalent of one-half of its cross-sectional area (one quarter 
in tension and one quarter in compression) can be fully stressed 
without exceeding the maximum permissible stress at the extreme 
fibre, whereas a curved plate, if bent to the proper shape, may have 
its whole cross-sectional area fully stressed in tension. Hence, 
although the cost of bending the plates is additional, the total cost 
may be reduced through the bent shape rendering permissible a 
less thickness of material than would be necessary with a flat plate. 

The bending of plates to form parts of cylindrical and other 
similar surfaces is easily and cheaply done by cold-rolling, but for 
spherical and such shapes the bending is more difficult, and, conse- 
quently, more expensive ; even these latter forms are useful in 
some cases, however, as will be seen presently. 

A spherical tank would give the greatest possible contents for 
the least area of shell, but would have the disadvantage of being 
closed ; it would also be difficult to support, and the work would 
be of a very costly nature. A hemisphere would be free from the 
first disadvantage, but not from the other two. There are other 
objections to such a form, which will present themselves on con- 
sideration, and all these together account for the fact that tanks of 
spherical shape are very seldom used. 

With elevated cylindrical tanks, however, advantage may some- 
times be gained by giving the tank a hemi-spherical dished bottom, 
so increasing the contents and saving the costly flat plate bottom 
and its supporting beams and joists. There are, of course, disad- 
vantages as well as advantages in this method, and the total saving 



ECONOMY OF FORIVI 35 

in outlay may be comparatively small, but it is worth considering. 
Sometimes the bottom is made conical, but the best shape would, 
clearly, be in the nature of a semi-prolate spheroid, giving no bending 
actions in the plates. This matter is more fully discussed in 
pages 52-57, 67-69, and in Chapter VIII, dealing with the tanks 
in which it is of use and importance. 

The next most economical form is the cylindrical, and many 
tanks, especially of large capacity, are made in this form. For a 
variety of purposes, however, the rectangular shape is both suitable 
and widely used, and we will consider it first as regards economical 
proportions. 

21. — Tanks Square on Plan. — Since a square is the greatest 
rectangle which a given perimeter can contain, it seems reasonable 
to assume that, for economy of sheeting area, one face at least 
should be square. Let the tank be square on plan, both its sides 
being h in length, and the depth d. Then the volume will be — 

V = b^d, (i) 

and the area of the shell — 

A = 4bd + b^ (2) 

supposing that there is no top or lid. 

V 

From (i), d = j^, and, inserting this value for d in (2) — 

^ b^ ^ b ^ 

Let the volume be assumed constant, and differentiate A with 
respect to b, to find the value of b which gives the least for A. 
Then — 

and for minimum A, the expression must be zero. Hence — 

2b^ = 4 V. 
.-. b^^-2V = 2b^-d, 
whence 

b-=2d (3) 

If the top or lid be included — regarding the roof as equivalent 
in cost, per unit of area, to the sheeting — equation (2) becomes — 

A = 4bd + 2b^, (4) 



36 TANK CONSTRUCTION 

the volume remaining unaltered, which gives as the most economical 

value of b — 

b = d (5) 

— i. e. a cubical form. 

Considerable departure from these proportions may be made, 

however, without much loss of economy (of area only, it must be 

remembered), as will be seen from the following numerical example. 

Take h = 10 ft., and ^ = 5 ft. Then, from (i) and (2) — 
V = 500 cub. ft., and A = 300 sq. ft. 

Now let ^ = 4 ft., V being constant. Then h'^ = - — sq. ft. 

h = V125 = ii-i8 ft. 
.-. A = 4 (4 X ii-i8) + II-I82 
= 178-88 + 125 = 303-88 sq. ft. 
If ^ = 3 ft., 62 = 166-67 sq. ft., b = 12-91 ft.— 

A = 154*92 + 166-67 = 321-59 sq. ft. 
If ^ = 6 ft., 62 = 83-33 sq. ft., b = 9-13 ft.— 

A = 219-07 + 83-33 = 302-4 sq. ft. 
li d = 7 ft., 62 = 71-43 sq. ft., 6 = 8*45 ft.— 

A = 236-7 + 71-4 = 308-1 sq. ft. 

The difference is more marked as the tank becomes shallower, 
but is small for a considerable range of variation, and advantage 
may be taken of this fact to save labour in manufacture. 

The conditions of this case are as indicated in Fig. 7, the varia- 
tions in proportions consequent upon an increase or decrease in 
the depth (from the relation b ^ 2 d shown in equation (3) to give 
minimum area of shell) being shown by dotted and chain-dotted 
lines respectively. 

We will now consider the case of a similar tank, but having a 
roof; and we will deal with it first on the basis of an assumption 
that the cost of the roof per square foot will be equal to that of 
the tank shell proper. 

For such conditions, equation (5) shows the cubic form to be 
the most economical as regards area of sheeting. To facilitate 
comparison, let us consider a tank having a capacity of 500 cub. ft., 
as in the example relating to a tank not covered at the top. 



ECONOMY OF FORM 37 

The cubic form will give length, breadth, and depth equal to — 

d = 1/500 = 7*94 ft., 

whence the area of the shell surface will be — 

A = 6 ^2 ^ 6 X 63 = 378 sq. ft., 

of which 63 sq. ft. will be in the roof, and 315 sq. ft. in the shell 
proper. 




Fig. 7. 

Keeping the plan square and the volume constant, the effects 
of making the tank shallower will be as follows — 

If ^ = 7 ft., breadth (or length) = h = ^ ^^^ = \/7r4=8-45 ft.— 

k = ^hd ^ 2})^ = 2h{2.d^h) = i6'9 (14 + 8-45) 
= 16-9 X 22-45 = 379 sq. ft., 

of which 71 '4 sq. ft. will be in the roof, and 307*6 sq. ft. in the shell 
proper. 



38 TANK CONSTRUCTION 

If ^ = 6 ft., h = >/5°^ = VSya = 9-13 ft.— 

A = 18-26 (12 + 9*13) = i8'26 X 21*13 = 386 sq. ft., of which 
83*3 sq. ft. will be in the roof, and 3027 sq. ft. in the shell proper. 
The effects of increasing the depth will be as follows — 

If ^ = 9 ft., b = V ^9^ = VSS'SS = 7'45 sq. ft.— 

A = 14-9 (18 + 7'45) = 14-9 X 25'45 = 379-2 sq. ft., 

of which 55*55 sq. ft. will be in the roof, and 323*65 sq. ft. in the 
shell proper. 

If i = 10 ft., b = y 5^^ = V5^ = 7-07 ft.- 

A = 14*14 (20 + 7*07) = I4'i4 X 27*07 = 382*8 sq. ft., 

of which 50 sq. ft. will be in the roof, and 332*8 sq. ft. in the shell 
proper. 

This case is illustrated in Fig. 8, the dotted lines showing the 
changes in the proportions due to increase or decrease in depth 
with constant volume and keeping the plan square. 

From the calculations it will be seen that as the tank is made 
shallower, the sheeting proper (i. e. in the walls and floor — the 
actual containing surfaces) becomes more efficient, approaching 
maximum economy as the proportions become more nearly the 
ideal b = 2 d oi equation (3). Reduction of the depth below half 
the breadth would, clearly, cause a rapid loss of economy in a roofed 
tank, for the sheeting proper becomes less efficient while the roof 
area increases as the square of the breadth — i. e. inversely as the 
depth. Increased depth, over a considerable range, is found to 
cause a relatively slight loss of economy in the whole area, but it 
should be noted that the loss in the sheeting proper is more than 
appears from the direct results, the roof area becoming less in 
relation to the whole. The most important thing to notice, however, 
is that appreciable departures may be made from the proportions 
which give the least shell area for a specified volume, without much 
increase in the area. Labour may often be saved by such means, 
and the cost of a tank actually reduced in consequence. As an 
instance, suppose the most economical depth for a certain proposed 



ECONOMY OF FORM 



39 



tank appeared, from application of the appropriate equation, to 
be about 6 ft. Now, plates of such width are difficult to obtain, 
and adherence to the stated depth would usually entail either some 
less advantageous arrangement of available plates, or the use of 
narrower plates in two strakes — both involving additional seams 
for riveting. If the depth were reduced to 5 ft., stock plates might 
be used, and the additional cost due to the slight increase in area 




Fig. 8. 

of the sheeting would be more than nullified by the reduction in 
riveting. 

Where the roof for a tank is to be of such form and construction 
that it will cost more (or less) per square foot than the sheeting 
proper, equation (3) cannot give dependable results. It is, however, 
a simple matter to obtain a suitable relation for such cases, by 
introducing the ratio borne by the cost of the roof per unit area to 
that of the sheeting proper. 

Knowing the specification or conditions in any particular case, 



40 TANK CONSTRUCTION 

it is always possible to form some estimate as to the probable cost 
of the roof per square foot (including all necessary bearers, purlins, 
or other supporting work, holding-down bolts, gutters, down-pipes, 
etc.) as compared with the probable average cost per square foot 
of the sheeting in the walls and floor. Such particulars can only 
be estimated, of course, but with intelligent application of the 
results of experience, the estimates may be made reasonably correct 
forecasts of the subsequent facts. In cases where some degree of 
refinement is desired, the estimates may be used to obtain a first 
set of proportions, and a sketch design prepared, to include all 
essentials, on that basis. A reliable estimate may then be made 
as to the relative costs of the roof and sheeting proper (the average 
for the latter) per square foot, and a more accurate relation obtained 
for the most economical proportions of the tank. 

In stating the conditions symbolically, the alteration in cost per 
unit area may be taken account of by assuming that no such altera- 
tion in cost occurs, but the area to be covered by the roof varied 
in the same ratio as the cost is actually varied. For instance, if a 
roof were likely to cost twice as much per square foot as the shell 
proper, we might imagine the roof made up of a double layer of 
ordinary sheeting, the total cost being the same, of course. 

Suppose a tank is to have a cheap form of roof, the total cost 
of which per square foot is estimated at half that of the walls and 
floor ; the cost of the tank and roof complete would be the same as 
though the cost of the roof per unit area were exactly equal to that 
of the shell proper, but the roof covered only one-half of the tank 
on plan. The equivalent area of sheeting would then be made up 
of the four walls, the floor, and half the area to be covered by the 
roof — 

K = ^hd+TSh^ (6) 

Inserting the value of d from equation (i), which still holds — 

A = 4_Y + 1-5 ^,2^ 

and differentiating with respect to h, regarding V as constant — 

dk 4V , ; 

'db=- h- +3^ 



ECONOMY OF FORM 4I 

whence, for minimum area of sheeting — 

4 V = 3 ^?3 _ 4 62 ^, 

and- b = ^^{d) (7) 

Stating the matter in a general form, suitable for application 
to any ratio of costs for roofing and shell proper, let r be the ratio 
borne by the cost of the roof per unit area to that of the shell proper, 
i. e. — 

cost of roof per unit area .q. 

cost of walls and floor per unit area * ' ^ J 

Then — 

A = 4bd-\-b^i + r) (9) 

= if + b^{T + r). 
Keeping V constant, and differentiating with respect to b — 

-M = - V + = * (^ + '')' 

whence, for minimum area of sheeting — 

4V = 2b^ (1 ^r) =4b^d, 

and — b ~ di j (10) 

Clearly, if r = i [i. e. the cost per unit area is constant for the 
roof and shell proper), b = d, ^s in equation (5), but whatever value 
may be assigned to r, equation (10) will give the most economical 
proportions for a tank square on plan under those circumstances, 
as regards area of sheeting. 

If it be desired to take into account a difference between the 
costs per unit area of the bottom (as well as the roof) and side 
sheeting, the ratio of these two costs might be represented by q, 
just as r is used in equation (8) for the roof. 

Equation (9) would then become — 

A =-. 4 & ^ + b'^{q ^r) (9«) 



42 TANK CONSTRUCTION 

Keeping V constant, and differentiating with respect to b — 

whence, for minimum area of sheeting — 

4 V = 2 b'^iq + r) =4b^d, 

^nd— b = d(^^-^^ (lOrt) 

22. — Tanks Rectangular on Plan. — ^Tanks of the form under 
discussion are often rectangular on plan, instead of square, and it 
will therefore be well, before passing on to the consideration of 
other forms, to investigate the relation between changes in the 
proportions and the consequent alterations in the shell surface for 
such cases. 

In order to avoid the trouble and complication of the work 
involved in dealing with three variables, let us suppose that the 
breadth is equal to the depth. The shape will then be as indicated 
in Fig. 9, the dotted lines showing the variations in the proportions. 

For a tank having no roof — 

\ = ld^, (II) 

and the area of shell surface — 

A = 3 / ^ + 2 ^2^ (12) 

where I = length of tank, and d = depth = breadth. 

V 

From (11), I = ~i2> ^^^' inserting this value for / in (12) — 

A = ^ ,^ + 2 d\ 

a 

Differentiating with respect to d, and regarding V as constant — 

^ _ _ 3 V 

dd~ ^2 + 4 ^, 

whence, for minimum area of sheeting — 

4d^ = 3y = 3ld^ 

and — I = "^ d (13) 



ECONOMY OF FORM 

Inserting this value lor / in equations (ii) and (12)- 



and — 



V = 4^3 



A = 6^2 



Fig. q. 



43 

(14) 
(15) 




For a volume of 500 cub. ft. (chosen so that the results obtained 
may be comparable with those of the two preceding examples) — • 



d^ = i 



V = -^ = 375 cub. ft., 

whence-^ 

d = -^5^ = 7-2 ft. and / = ^ ^= 4 X 7-2 . 
Then — 



9-6 ft. 



3 3 

A = 6d^ = 6 X y'2^ = 6 X 51*84 = 3ii'04 sq. ft 



44 TANK CONSTRUCTION 

Comparing this result with the 300 sq. ft. obtained for the 
unroofed tank square on plan, it will be seen that the most econo- 
mically proportioned tank rectangular on plan requires about 
3*7 per cent, more area of sheeting than does the most economically 
proportioned tank of the same capacity square on plan, both tanks 
having no roof. 

If rf = 6 ft., / = ^-> = 13-9 ft., and A = 250-2 + 72 = 322*2 sq. ft. 
If ^ = 5 ft., / = ^ - = 20 ft., and A = 300 -f 50 = 350 sq. ft. 
Ud = S ft., / = 500 ^ y.g f^^ ^^^ ^ ^ jg^.2 _|_ 128 = 315-2 sq. ft. 

If ^ = 9ft.,/ = ^ = 6*2 ft., and A = 167-4 + 162 = 329-4 sq. ft. 

Thus, by comparison of these results with those of the example 
in Article 21, it will be seen that the increases in area vary from 
about 4 to 10 per cent., except the case where the length is four 
times the depth, in which the increase is nearly 17 per cent. It is 
quite possible, however, that this latter case might, in spite of the 
relatively large increase in the shell surface, give a cheaper tank 
than the others, for the walls and bottom could be made, in it, of 
plates 5 ft. in width, requiring no seams other than those where 
the walls meet the floor and each other, whereas most of the other 
cases would involve additional seams and riveting. 

For a tank of this shape having a roof, and using r to denote 
the ratio of costs per unit area for roof and shell proper, as in 

equation (8) — 

A = / ^ (3 + y) + 2 ^2 (16) 

- = ^ (3 + ^) + 2 ^2 
Differentiating with respect to d, as before — 

whence, for minimum area of sheeting— 



d^[ -^ ] = \ = ld\ 
\3 + rJ 



ECONOMY OF FORM 45 



and- i = 'i[^-l-r) (^7) 

li r — 1 — i. e. the cost per unit area constant throughout, — / = 
d, and the form giving maximum economy of sheeting is (as might 
be expected from the foregoing considerations) a cube. 

There is no need to work further examples regarding the effect 
of variations from the cubical proportions, for those relating to 
the tank square on plan will apply. 

With any particular value of r appropriate to an individual case, 
the ideal proportions (as regards economy of shell area) may be 
calculated from equation (17), and it will be found that, as in the 
other cases investigated, considerable departure from those pro- 
portions may be made when necessary or desirable, without much 
increasing the area of the sheeting. 

If it be desired to take into account a difference between the 
costs per unit area of the bottom and side sheeting also, let the ratio 
of these two costs be represented by q, just as r is used for the roof. 

Then, equation (16) would become — 

A = ld{2 + q + r) + 2d^ . . . . (16a) 
= ^ (2 + ^ + ;-) + 2 ^2 

Differentiating with respect to d, as before — 
whence, for minimum area of sheeting — 



d^ , ^ , ) = y = ld\ 
and — 



A long, narrow, and shallow tank covers more ground than one 
of the same capacity more nearly approaching the cubical form, 
and this is sometimes an important matter; sometimes, again, a 
long, narrow tank can be conveniently placed over an existing 
building, whereas a square plan would encroach upon valuable 
yard space. All these matters, as well as many others of a similar 



46 TANK CONSTRUCTION 

nature, must be considered in each case before any particular shape 
or set of proportions can be laid down as the most economical. 

23. — Cylindrical Tanks. — To examine the cylindrical form as 
regards area of sheeting for cubic capacity, suppose the diameter is 
d, and the height h, the bottom and roof (if any) being considered 
first as flat and costing the same per unit area as the side sheeting. 
Then the volume, or capacity, will be — 

V = 07854 d^ h, (18) 

and the area of shell surface, with no roof — 

A = 3"i4i6 dh -{- 07854 d'^ . . . . (19) 

V 
From (18), h = ^^ — -j^, and inserting this value for h in (19) — 



A = -^/f "^ ^ + 07854 d^ = -f + 07854 d^ 



3-1416 ^V , ^_Q_ ^2_4V 
07854 d'^ 

Differentiating with respect to d, and regarding V as constant — 

d K 4V, o J 

j-rf = - i^ +^■5708'^' 

whence, for minimum area of sheeting — 

1-5708 ^3 := ^ V = 3*1416 ^2 }i^ 

and h = - {20) 

2 ^ ' 

Inserting this value for h in equations (18 and (19) — 

V = 0-3927 d^ (21) 

and A = 2-3562 d^ (22) 

The proportions just deduced are indicated, for convenient 
reference, in Fig. 10. 

For a volume of 500 cub. ft. (chosen so that the results obtained 
may be comparable with those of the preceding examples for 
rectangular tanks) — 



whence — 



d^ = -^ = 1273*2 cub. ft., 

0-3927 ^-^ 



d = -^1273-2 = 10*83 ft., and h = = 5-42 ft. 



ECONOMY OF FORM 



47 



Then — ■ 

A = 2*3562 ^2 = 2-3562 X ii7'3 = 276-4 sq. ft. 

Comparing this result with the 300 sq. ft. required for the un- 
roofed tank square on plan, there is a saving of 23-6 sq. ft. in 300, 
or about 7-87 per cent, in the area of sheeting, but to set against 
this there is the additional cost of cutting the bottom plates to the 
circular curve, setting out the riveting for the circumference of 
these plates (and for the bottom curb angle) on curved pitch 
lines, and bending the side plates 
to give the cylindrical form. Also, 
both bottom and side plates for 
cylindrical tanks are more awkward 
and troublesome to handle, and 
require much more space in vehicles 
for haulage and transport, than do 
fiat rectangular plates. 

To investigate the effects of 
departure from the proportions of 
equation (20), giving the least area 
of sheeting for this case, let us consider four examples, two having 
the diameter more, and two less, than 10-83 ft., the volume being 
kept constant at 500 cub. ft. 

500 




Fig. 10. 



If 



^ = 12 ft., h 



= 4-42 ft., and A 



If d=iz ft., h = 



0-7854 X 144 
= 166-7 X ii3'i = 279-8 sq. ft. 
500 



If 



If 



^ = 10 ft., h = 



0-7854 X 169 

= I53"9 X 132*7 = 286*6 sq 

500 



^ = 9 ft., h = 



0-7854 X 100 

= 200-1 + 78-5 = 278-6 sq 
500 



X 



= 3*77 ft., and A 
ft. 
6-37 ft., and A 

ft. 
7-87 ft., and A 



0*7854 

= 222*7 ~r 63*5 = 286*2 sq. ft. 

Hence, a variation (either increase or decrease) of nearly 20 per 
cent, from the diameter giving the minimum area of sheeting, causes 



48 



TANK CONSTRUCTION 



an increase of only 3*69 per cent, in the area of the shell. Full 
advantage should be taken of this fact to secure the most economical 
proportions for each particular tank, for by regulating the height 
(within reasonable limits, of course) to suit convenient widths of 
plates, it is often possible to save one complete circumferential 
seam, and several vertical ones, by making the number of strakes 
one less than would otherwise be necessary. 

With a fiat roof costing the same per unit area as the side sheeting, 
V will be as before, but the area of shell surface will be — 

A = 3-1416^/? + 1-5708^2 .... (23) 




Fig. II. 

Inserting in (23) the value of h from (18) — 

A V 
A = ^^ 4- 1-5708 ^2. 



Differentiating with respect to d, and regarding V as constant — 

t:/- = - V + 3-1416 d, 



d d 



d^ 



whence, for minimum area of sheeting — 

3-1416 d^ = /[\ = 3-1416 ^2 h^ 

and, obviously — 

h = d (24) 

These proportions are, like those for other cases, indicated in a. 
diagram for easy reference, the illustration here being Fig. 11. 



ECONOMY OF FORM 49 

Inserting the value for h from (24) in equations (18) and (23) — 

¥ = 07854^3 (25) 

and A = 4'7^24 d^ (26) 

For a volume of 500 cub. ft. (chosen again for the purpose of 
comparison) — • 

d^ = -^ — =^ 636-6 cub. ft., whence d = -^636-6 = 8*6 ft. 
07854 

Then, A = 47124 d^ = 47124 X 73*99 = 3487 sq. ft., of which 
58'i sq. ft. will be in the roof, and 290*6 sq. ft. in the shell proper. 

Comparing this with the roofed tank square on plan, which 
required 63 sq. ft. for the roof and 315 sq. ft. for the shell proper, 
giving a total area of 378 sq. ft., the roofed cylindrical form shows a 
saving of 293 sq. ft. in 378, or about 77 per cent, of sheeting surface, 
to set against the extra cost of labour and transport for the material 
of the cylindrical tank. 

It is well to investigate the effects of departure from the pro- 
portions h = d, of equation (24), keeping the volume constant at 
500 cub. ft. 

If ^ = 10 ft., Ji = — ^ = 6'37 ft., and A 

07854 X 100 ^^^ 

=-- 200-1 + 157-0 -^ 357-1 sq. ft., 

of which 78-5 sq. ft. will be in the roof, and 278-6 sq. ft. in the shell 
proper. 

If ^ = II ft., h = 6~ — = 5'26 ft., and A 

0-7854 X 121 ^ 

= 181-9 + 190-1 = 372-0 sq. ft., 

of which 95-0 sq. ft. will be in the roof, and 277-0 sq. ft. in the shell 
proper. 

If d —- y ft., h = ^ = I2-QQ ft., and A 

0-7854 X 49 y^ > 

= 285-9 + 77'^ = 362-9 sq. ft., 

of which 38-5 sq. ft. will be in the roof, and 324-4 sq. ft. in the shell 
proper. 

If d = 6 ft., h = — ^^^ r- = 17-68 ft., and A 

0-7854 X 3^ ^ 

= 333'4 + 56-5 = 389*9 sq. ft., 



50 TANK CONSTRUCTION 

of which 28'3 sq. ft. will be in the roof, and 361*6 sq. ft. in the shell 
proper. 

Hence, increasing the diameter by 27*9 per cent, increases the 
total shell surface by only 67 per cent., and reducing the diameter 
by 30'2 per cent, increases the area of the sheeting by ii'8 per cent. 
It will be seen from the calculations that as the tank is made 
shallower, the sheeting proper (in the cylindrical wall and floor) 
' becomes more efficient until the proportion d = 2 h oi equation 
(20) is reached, after which, further reduction in the depth would 
cause a rapid falling off in the economy of sheeting area. Increasing 
the depth causes a relatively greater loss of economy, and this loss 
is, to a large extent, a loss of efficiency in the sheeting proper. 

A point worthy of notice in passing is the fact that, so far as 
regards economy of sheeting area only, the loss in an unroofed tank 
(rectangular or cylindrical) is most marked as the tank becomes 
shallower — i. e. more slab-hke ; and in a roofed tank as the tank 
becomes deeper — i. e. more rod-like. As has been shown, there 
are other and important considerations to be taken into account, 
but this point is of real interest and importance, and we shall have 
more to say concerning it presently. 

The roofs of cylindrical tanks are nearly always made convex 
(the surface being usually spherical), with the object of thro-wing 
off rain, condensation water, and other corrosive solutions. The 
roof sheeting is usually quite thin — 14 B.W.G. being a commonly 
used thickness — and is carried upon light-framed trusses spanning 
from side to side, or radiating from a central post to the circum- 
ference. It is often advisable to countersink all rivets in the roof 
sheeting at the outer surface, thus reducing the liability to corrosive 
actions. 

The actual area of the roof sheeting may, then, be appreciably 
more than that of a horizontal section through the tank, and the 
extra work in dishing the plates, combined with the cost of the 
supporting trusses, and operating against the effects of using lighter 
sheeting, may make the cost of the complete roof per square foot 
either more or less than the average cost per square foot of the shell 
proper. To allow for this in determining the proportions which 
will give maximum economy as regards the area of sheeting, let r 
denote the ratio of the costs per unit area for the roof and shell 



ECONOMY OF FORM 5 1 

proper, as in equation (8), and let the altered cost be allowed for 
as though it were an alteration in the effective area at uniform cost. 
Then, equation (23) becomes — 

A = 3-1416 dh + 07854 d^ijL -^ r) . , (27) 

■ =^ + 07854^2(1 _|.^)^ 

Differentiating with respect to d, and regarding V as constant — 

jj = - ^^. + 1-5708 i (I + »-), 

whence, for minimum effective area of sheeting — 

4 V = i"57o8 d"^ (i + r) = 3'i4i6 d"^ h, 

and ^^^i^"^} '^^^ 

Clearly, if y = i {i. e. the cost of the complete roof per unit area 
of projected surface, or of ground covered, equal to that of the actual 
containing surfaces on the average), h = d, which agrees with 
equation (24). 

Equation (28) should be compared with equation (10) for a tank 
square on plan with a roof, and their similarity noted. 

If it be desired to take into account a difference between the 
costs per unit area of the bottom and side sheeting, the ratio of 
these two costs might be represented by q, just as r is used for the 
roof in preceding cases. Equation (28) would then become — 

" = 'i{'^-]. (29) 

from which it is clear that if the bottom and roof both cost less per 
unit area than does the side sheeting, the proportions for least area 
of sheeting will give h less than d, and vice versa. 

Horizontal cyhndrical tanks, like boiler shells in appearance, 
are sometimes used where a comparatively small capacity for storage 
is required, and for the carriage of liquids on railway trucks. These 
would provide a typical instance for the application of equations 
(23) to (26) inclusive, or, if the ends be dished, equations (28) and 
(29). For railway purposes, however, considerations of limiting 



52 TANK CONSTRUCTION 

over-all dimensions arc of more importance than that of economy in 
shell surface, and the latter is therefore sacrificed. In other cir- 
cumstances, however, the facts deduced above are at least worth 
considering. 

Cylindrical tanks, though economical in many ways, sometimes 
have the disadvantage of occupying more ground surface than 
would be required for a square or rectangular tank, because of the 
awkwardly shaped corner pieces left when a cylindrical tank is 
fitted into a rectangular space not much more in diameter than the 
tank. Where there is plenty of space, however — as there usually 
is on the roof of a building, for instance, — they may be made a very 
efficient form of construction, and should be used more freely than 
they are. 

One important advantage is possessed by cylindrical tanks 
as compared with the rectangular form, in that the cylindrical side 
plates need no internal staying. The ordinary theory for " thin 
cylinders " is used, as will be explained later, for their design, and 
although it might appear that the side sheeting of a tank (say) loo ft. 
in diameter is practically flat, the results of experience seem to 
indicate that the theory is justified, even for diameters much larger 
than that instanced, the liquid pressure internally causing the plates 
of each strake to be stressed in tension, with no appreciable bending 
action except such as is due to secondary stresses. Here and there 
one comes across a tank in which the designer, evidently feeling 
doubtful, has provided some sort of staying, but it is frequently 
found that the stays are so arranged and proportioned that they 
could not be of any real assistance in stiffening the side plates against 
bending. 

24. — Cylindrical Tanks with Dished Bottoms. — We have not yet 
considered the question as to what is most likely to be the most 
suitable shape for the dished bottom to a cylindrical tank from the 
point of view of stress limitation ; but some idea as to the economy 
of such bottoms, as regards area of sheeting, may be gathered from a 
consideration of a hemispherical and a conical bottom, observing 
the influence of variations in the apex angle in the latter case, and 
ignoring the effects of bending stresses in the plates. 

First, in the case of a hemispherical bottom, as indicated in 
Fig. 12, if d be the diameter of the cylindrical tank, the capacity 



ECONOMY OF FORM 



53 



d 




Fig. 12. 



of the bottom will be V,, =d'^\^\ = 0-2618 d"^, and the area of the 

sheeting Ab = d'^ y-) = i*57o8 d"^. So, by doubhng the area of 

the bottom sheeting, as compared with the flat- 
bottomed tank, additional storage capacity of 
©•2618 d"^ is obtained with the hemispherical 
bottom, and the joist system for supporting the 
flat bottom is avoided. To set against this 
saving, however, there is the extra cost of 
dishing the plates, increased and more difficult 
riveting and caulking, and curved girders to 
carry the tank. 

For obvious reasons, dished bottoms are 
used on elevated tanks only. 

A convenient method for comparing the 
storage efficiency of these dished bottoms is to determine the depth 
of the liquid they contain, assuming that liquid uniformly distributed 
over the sheeting surface. Thus, with the hemispherical bottom, 
the capacity is 0*2618 d^, and the area of sheeting i"57o8 d'^. If 
the sheeting could be laid out to form a flat 
surface, and liquid having a volume equal to 
the capacity of the bottom were spread over 
the fiat surface, being supported at the sides by 
auxiliary walls (or frozen to a solid), the liquid 

would form a slab, of depth D^ = - o 70 = ^• 

^ i'57o8 d^ 6 

This depth Ds (the sufhx s indicating that it 
relates to the spherical bottom) might well be 
termed the " effective storage depth of the 
sheeting," and it may be employed with ad- 
vantage in comparing not only dished bottoms, 
but also tanks themselves, of different forms 
and proportions. 
With a conical bottom', as in Fig. 13, the capacity of the bottom 

= 0"26i8 rf2 g^ where 8 is the " drop 









r/ ■> 




C/t >■ 







Fig. 13. 



will be V. 



12 



cone, as indicated in the sketch. 



of the 
The area of the sheeting will be 



54 TANK CONSTRUCTION 

Ah = "^x/s^ + "^^ = 07854 d VJW~-^'d\ If 8 = ^ (as for the 

hemispherical bottom), V^ = 0"i309 d^ — i. e. just half that for the 
hemisphere, — and Ag = 07854 d"^ V^ whence the " effective storage 

1 XT- »» T^ 0*1300 d^ d d 

depth Dc = — ;^'^ <; — 7- = 7- = 0—0. 

^ 07854 ^2 1/2 6 V2 8-48 

If S = ^, then Vb = 0-2618 d^, and Ar = 07854 d'^ V5, whence 

^" 671* 
If 8 = 1*5 f^, then Vb = 0-3927 d^, and A,, = 0-7854 d'^ Vio, whence 
D =^ 

6-32 

If 8 = 2 ^, then Vg = 0*5236 d^, and A^ = 0-7854 d"^ '\/i7, whence 

6-18* 
If 8 = 3 (^, then Vg = 0-7854 d^, and A^ = 0-7854 ^2 A/37, whence 



. Dc = 



D. = 



6-08* 



The last three (certainly the last two) instances are inadmissible 
for practical purposes, but they serve to illustrate the comparison 
of " sheeting efficiencies " for the two forms. The proportion h = d 
would be fairly suitable for practice, and then, it should be noticed, 
the capacity would be equal to that for the hemispherical bottom, 
while the area of the sheeting would be 1-7562 d"^, as against 1-5708 d"^ 
for the hemisphere — not a very large difference in actual area with 
tanks of such diameters as are likely to be suitable for dished bottoms, 
while the labour in bending the plates, and also in riveting and caulk- 
ing, would be less with the cone than with the hemisphere. Moreover, 
the difference in area for an actual case would probably be less than 
that shown by calculations on the above basis, for the bottom 
(whether hemispherical or conical), with the methods of construction 
usually employed, could not well spring from the cylindrical wall 
of the tank. If it did, some form of external bracketed ring con- 
struction would be necessary, to provide a seating for the trans- 
mission of the entire weight to the curved supporting girders, and 
this would be both costly and unsightly. It is usual to place the 



ECONOMY OF FORM 55 

supporting girders beneath the cyUndrical wall, or sometimes, even 
a few inches nearer to the centre of the tank, and the dished bottom 
then springs from the inner edge of the girder ring; hence, the d 
for the bottom will be less than the diameter of the cylinder. 

For a cylindrical tank having some form of roof and a hemi- 
spherical bottom, as indicated in Fig 12, the general investigation 
for economy of form might be as follows. Adopting the symbols 
used in the preceding cases, and denoting the height of the cylindrical 
portion by h — • 

4 2\3 8/ 4 12 

whence — - d^ h = V d^, 

4 12 

J J 4 y d 

and — h ^ ^ 



IT 



d' 3 



A = 7rdh-{-'^d^r+^(7rd^q) 

4 2 ^ ^^ 

Substituting the value of h from above — 

d 3 4 ' 2 ^ 

Differentiating with respect to d, and regarding V as constant — 

d A 4 V 2 TT d TT d r , 

d A 
For minimum area of sheeting, j-j = O ; whence — 

4V TT dr , J 2 IT d 
d^ 2 ^ 3 

J , TT d TT d r , ^ 2 IT d 

3 ^ ^ 3 
So that — h=^d{-\-q — Tj (30) 

It should be noted that, in the foregoing investigation, the area 
of the roof has been taken as that of a horizontal section of the tank 
proper. The object of this is to leave the result applicable to any 



56 TANK CONSTRUCTION 

form of roof, and it is only necessary to observe that the \ahie 
employed for r must take into account any increase in area for the 
jTOof beyond that of the tank section — in other words, r must be 
evaluated on the basis of roof-cost per square foot of actual tank 
(horizontal) section. 

For a cylindrical tank having some form of roof and a conical 
bottom, as indicated in Fig. 13, the investigation for economy of 
form might be as follows — 



4 3\4 / 

whence — // 



4 3\4 

4V_8 
■^d^ 3 



A = TT ^ A + - ^' ^ + ^ Vd^ 4- 4 82 
4 4 

Substituting the value of h from above, and writing k d instead 
of 8— 

"•34 4 

Differentiating with respect to d, and regarding V as constant — 

d K _ 4V 2ir-kd'7rdrTTdq Vi + 4 k^ 
Td ^ ~ d^ 3 ^ + ~2~ "• 2 

d A 
For minimum area of sheeting, -^ , — O ; whence — 

'r d q Vi + 4 ^^ 2 kd\ 





4^'-, 
^52 -" 


•*• 




whence — 


h = 



dr d q Vi -i- 4 k- 2 kd 



223 

'r q Vi + 4 ^^ 



i:-,^'-^-'' -k): 



Here, again, the value employed for r must be that obtained 
on the basis of roof -cost per square foot of actual tank (horizontal) 
section. 



ECONOMY OF FORM 



57 



To judge from the remarks of the few writers who have dealt 
with dished bottoms for tanks, appearance would seem to be the 
most important (if not the only) factor in their design. This, of 
course, is by no means the case. In some circumstances the stand- 
pipe or water tower is an important public structure, and is so placed 
as to form a very prominent and noticeable object ; and appearance 
is of considerable importance in such cases, though the efforts of 
some designers to make water towers " pleasing " are rather amusing 
— to those who are not called upon to bear the cost. 

The appearance of such a structure depends largely upon its 
altitude, position, dimensions, and proportions, and it will be shown 
later that ugliness may be avoided by 
considering these matters, rather than by 
adopting one particular form for all con- 
ditions and circumstances. The ordinary 
and obvious principles of natural growth 
and formation are the best guide to follow 
in these and similar points, and it cannot 
be too strongly urged that the first principle 
of beauty in architecture is true suitability 
to purpose. It is a pity that engineers 
do not pay more attention to such simple 
and interesting matters, for there is really 
no reason why a tank, or any other strictly 
utilitarian structure, should be offensive to 
the eye and a reproach to the profession. Nothing need be sacrificed 
in design which could make for efficiency in working, or the mini- 
mising of the costs of manufacture and erection. Indeed, there is 
good reason to believe that a structure proportioned on the lines 
of natural growth will of necessity be economical and efficient, 
provided the application be made intelligently. 

25. Rectangular Tanks with Trough Bottoms. — A form which, 
though seldom used, might well be considered where the conditions 
are favourable, is a rectangular tank with a trough bottom, as indi- 
cated in Fig. 14, which shows a cross-section of the tank and trough. 
If carried on stanchions or piers, the side walls of the tank may be 
arranged to act as the girders for transmitting the loads between the 
supports. Such a form would evidently be suitable for elevated 




Fig. 14. 



58 TANK CONSTRUCTION 

tanks in which, owing to circumstances of available space, the length 
must be great as compared with the width. The plates forming 
the trough could be easily bent to the required shape, and the erec- 
tion and riveting would be simple. With vertical flat ends to the 
trough, it would probably be necessary to provide stiffening for 
the plates, against the pressure of the contained liquid, but this 
is a simple matter. 

The trough might be semi-elliptical in cross-section, or some 
convenient modification of that curve might be adopted. A semi- 
cylindrical trough would give the greatest capacity as compared 
with the area of sheeting, but, as will be shown presently, might 
cause more bending actions in the plates than would the semi- 
elliptical shape, owing to the greater depth of the liquid at the middle 
of the trough. 

It should be noticed that such a trough cannot be properly 
regarded as " flexible." To consider a strip of the trough-sheeting 
between two sections at right angles to the length of the tank, and 
treat it as though it were a chain, with loads applied at the points 
of contact between the links, is to make an assumption which cannot 
be realised. A chain would be free to take up that shape imposed 
upon it by the loading, with no resistance other than the slight 
friction between the links, whereas a solid steel plate, of such thick- 
ness as is practicable for tank work, is not fr-ee to change its shape, 
and any tendency to cause such change of shape would induce more 
or less severe stresses in the material by reason of the bending action 
set up. Moreover, with a chain, variations in the loading would 
cause changes in the shape of the chain, whereas, in a trough- 
bottomed tank, although the loading may vary both widely and 
frequently through alterations in the head of the contained liquid, 
if appreciable changes of shape occurred in the riveted plates forming 
the trough, the seams would not remain tight against leakage. This, 
of course, applies equally to all curved or dished bottoms. Probably 
the best method for designing in such cases is to determine the shape 
which will give the least bending actions in the curved plates under 
the greatest pressures, and then to provide such stays and framing as 
will prevent undue stresses and excessive changes of shape with the 
different conditions of loading possible or likely to occur. 

The significance of this will be clear on reference to Fig. 15, which 



ECONOMY OF FORM 



59 



represents the cross-section of a trough-bottomed rectangular tank. 
Suppose the plates forming the trough are so thin as to be perfectly 
flexible, and that, with the tank full, they take the shape indicated 
in the sketch (a). Now, if the liquid fell to the level A A, as at (6), 
the portions of the sheeting A B would become straight, and it 
is clear that riveted seams — particularly circumferential seams — 
subjected to such changes of shape could not be relied upon to remain 
tight. Plates of ordinarily practicable thickness would, to some 
extent, resist this tendency to change of shape, and thus stresses due 
to the bending action would be added to the direct tensile stress. 
As the loading decreases in magnitude, the direct tensile stress 
in the plates is, of course, reduced, and the object should be to so 





Fig. 15. 



arrange that the additional stresses due to bending, under a reduced 
loading, do not more than counterbalance the corresponding 
reductions in the direct tensile stresses. 

In Fig. 15 an exceptional case has been chosen, solely for the 
purpose of illustrating clearly the effects of such changes in shape, 
and the change is exaggerated. This affects the point in degree only, 
however, and not in principle, for although the effects may be reduced 
in magnitude by a judicious choice of the most suitable shape for 
the trough (or dished) bottom, they cannot be eliminated. 

Here an important point of difference between rectangular 
and cylindrical tanks having trough or dished bottoms should be 
noticed. In the rectangular tank of Fig. 15 (a), the contained liquid 
in the tank proper will cause an outward horizontal thrust to act 



6o 



TANK CONSTRUCTION 



upon both the side walls, and some provision for resisting these 
thrusts is necessary to ensure stability. With a cylindrical tank no 
need for such additional provision arises, because the outward 
pressures at each level act uniformly in directions radiating from the 
centre of the tank, and the outward thrusts are resisted by simple 
circumferential tensions in the sheeting. Further, when the liquid 
fills only a portion of the trough in a rectangular tank, as at (b) 
in Fig. 15, there will be an inward pull at the bottoms of the side 
walls, tending to draw the walls together, and although these inward 
pulls are likely to be of small magnitude in a properly designed tank, 
they must be provided for. 




/a) (b) 




Fig. 16. 

The walls of the rectangular tank of Fig. 14 may be supported 
against horizontal forces by means of transverse stays at the top 
and bottom, as indicated at {a) in Fig. 16 ; or, preferably, by framed 
bracing, as shown at (b) in that sketch. These stays or frames should 
be spaced at a convenient distance apart, and the walls provided with 
sufficient strength and stiffness to resist the horizontal forces over 
this distance. The most suitable distance between the transverse 
stays or bracings must vary with, and depend upon, such conditions 
as the height of the side walls; and there will be, for every case, 
one spacing which is more economical than any other. With trans- 
verse stays very close together, the side walls would need little 
or no additional stiffening, but the cost of the stays might be heavy. 
On the other hand, with the stays far apart, while the cost of the 
stays might be trifling, considerable expense would probably be 
incurred in stiffening the side walls sufficientl}^ to enable them to 



ECONOMY OF FORM 6l 

properly resist the outward pressures between the stays. To keep 
down the cost of the stays it is necessary to use as few of them as 
possible, and to avoid extra expense in stiffening the side walls 
of the tank it is necessary to use as many lateral stays as possible. 
These opposing considerations will determine the most economical 
spacing for the stays, and it should be borne in mind when dealing 
with such matters that a heavy transverse stay or .framed bracing 
need cost but little more to make and fix than does a light one, 
the total cost of such stays or bracings in a tank being much more 
nearly proportional to their number than to their individual or 
aggregate weights ; and also that, by means of the intelligent dis- 
posal of material, the side walls of a tank may be so constructed 
as to possess a reasonable degree of lateral strength and stiffness, 
instead of practically none, for little or no increase in the cost. 

With an ordinary fiat-bottomed rectangular tank, the floor acts 
as a sufficient tie to the side walls at the bottom, stays to the upper 
parts only of the walls being needed, and whatever increase of cost 
for lateral staying results from the use of such a form as that indicated 
in Fig. 14 must be regarded as tending to discount the advantages 
of a trough instead of a flat bottom, supported on joists — provided, 
of course, that the staying be designed with proper regard for 
efficiency and economy. 

In tanks, the contained substance being always liquid, the out- 
ward thrusts and inward pulls referred to above will always be 
symmetrical, and hence, there are no unbalanced horizontal forces 
applied to the structure or its supports from the mere storage of the 
substance, and other than forces from such external agencies as 
wind pressure, with an elevated tank of the section shown in Fig. 14. 
With bunkers and silos, to contain granular material which may stand 
at comparatively steep angles with the horizontal, unbalanced 
forces of considerable magnitude may be set up unless means for 
their prevention — usually by subdividing the storage space into 
relatively narrow cells — be adopted. 

Matters would not be much improved, with the rectangular 
tank, by the use of a segmental trough, as indicated in Fig. 17, for 
the curved plates, unless they were of much greater thickness than 
required for containing the liquid, could not provide adequate 
support to the side walls against horizontal forces. Moreover, 



62 



TANK CONSTRUCTION 



a segmental trough has two disadvantages as compared with one 
semi-elHptical in cross-section with the major axis of the elhpse 
vertical. First, though the cost of the curved sheeting would prob- 
^ ably be only shghtly reduced, there would be a 

very large proportional loss of storage capacity ; 
and, second, the connections of the trough plates 
to the tank walls would be troublesome and 
costly to make properly satisfactory and reliable. 
For the purpose of investigating the effects 
of a semi-elliptical trough bottom to a rect- 
angular tank, as regards storage capacity and 
sheeting surface, it will be sufficient to use the 
approximate relations for the ellipse — ■ 



K 



\ 




Fig. 17. 



Perimeter = - (major axis + minor axis) ; 



Area 



(major axis x minor axis). 



If h represents the breadth of the tank (Fig. 14), the minor axis 
of the ellipse will be h, and the semi-major axis may be conveniently 
denoted by 8, the " drop " of the trough. Then, taking h, d, and 8 
in lineal feet, we may calculate for one foot run of the tank and 
trough, so that areas will be in square feet, and volumes in cubic 
feet. It should be noticed that this basis for calculation assumes 
that the length of the tank is so great as compared with its width 
that the sheeting in the ends is insignificant in comparison with 
that in the sides. The case for a shorter tank will be considered 
presently. 

Ignoring the question as to whether the tank is to have a roof 
or not (since the roof would be the same so long as the breadth is 
unchanged), the area and volume of the combined tank and trough 
per foot run will be — 

K = 2d^\\ 1-5708 (6 -f 2 8) } = 2 ^ -f 07854 (6 + 28); 

y = hd ^\\ 07854 (^ X 2 8) } = Zj ^ + 07854 (6 8) 
= M^ + 07854 8). 

Comparable with these are : K = 2 d ■\- h, and V = h d, for the 
simple flat-bottomed rectangular tank. 



ECONOMY OF FORM 63 

If the volume of the trough is to be equal to that of the tank 
proper, we shall have : 07854 (b S) = b d, whence — 

8 = — o — = 1*27 d. 
07854 ^ 

Inserting this value for 8 in the expression for the area of the 
sheeting — 

K = 2 d -\- 07854 {b + 2*54 d) = 2 d -\- 07854 b -\- 2 d 
= 4 ^ + 07854 b. 

Now, to double the volume of the flat-bottomed tank by doubling 
the depth would require a sheeting area of 4 ^ + b, and hence, the 
trough would give a saving in the area of sheeting equal to 

(4 ^ + ^) — (4 ^ + 07854 b) = 0-2146 b. 

This shows the extent to which, with a fixed breadth, the semi- 
elliptical form is more economical as regards sheeting area, for a 
given volume, than the rectangular flat-bottomed tank. The semi- 
elliptical trough has also the advantage that, when full, the plates 
may be subjected to simple tension, whereas the flat sides of the 
rectangular form are called upon to resist bending actions, and must, 
therefore, be either well stayed or of greater thickness. Moreover, 
supporting joists are required with the flat bottom. 

Hence, it would appear that considerable saving may be effected 
by the use of a trough bottom, and that the saving would be most if 
the rectangular portion were rejected altogether, the storage capacity 
being entirely in the trough. If that were done, however, the tank 
would be difficult to support, and the cost of the additional girders 
and work rendered necessary would outweigh much of the saving. 

Perhaps the best method, where circumstances permit, would be 
to make the vertical side walls of sufficient depth to form the sup- 
porting girders only, putting all the remaining capacity into the 
trough. 

If the trough is to have n times the capacity of the simple tank, 
the breadth being, of course, the same for both — 

07854 b B = nb d, whence : — 8 = d (i'2y n), 

giving the area of sheeting for the trough — 

Ae = 07854 {b + 2*54 n d) = 2 7i d -\- 07854 b. 



64 TANK CONSTRUCTION 

To give the simple tank 7i times its original volume by increasing 
the depth would require a plate area oi 2 n d -\- b, and the saving 
in sheeting area is again 0"2i46 b. 

Apparently, then, the saving in the area of sheeting is independent 
of the depth d, and hence it might seem that economy is to be secured 
by making the tank as broad as possible. This is true up to a certain 
limit only, however, and it will be seen presently that the best results 
are to be obtained when the breadth and depth are in a particular 
relation to each other. 

It will be well to examine briefly the effects of variations in 
the proportions of the cross-section for the rectangular trough- 
bottomed tank, first taking the case in which the length is great 
as compared \\dth the breadth. 




Fig. 18. 

From the expressions obtained above, it would appear that 
economy of sheeting area, with a semi-elliptical trough, is to be 
obtained by making the breadth as large as possible ; but a little 
consideration will show that this is not true beyond a certain limit. 
Those expressions were based upon the approximate relation for 
the perimeter of the ellipse, and this is the reason for the erroneous 
indication of great breadth as tending to economy of sheeting area. 
The approximate relation gives reasonably good results where the 
major and minor axes are not widely different, but cannot be relied 
upon where the ellipse is long and narrow. A single instance 
will suffice to show the error of the approximate relation in 
extreme cases. Consider the cross-section of an unroofed 
rectangular tank 12 ft. in width and i ft. in depth, as indicated in 
Fig. 18, and compare it with the semi-elliptical trough of equal 
breadth and capacity also shown. Now, the approximate relation 
would give the area of sheeting for the trough per foot run as 07854 
(12 + 2 '6) = 1 1 "4 sq. ft. — i. e. a curved line less in length by one- 



ECONOMY OF FORM 05 

twentieth than the straight hne between the same terminal points, 
which is clearly untrue. As the major axis becomes greater and 
greater as compared with the minor axis, it is obvious that there 
will, in fact, be less and less difference between the sheeting areas 
per foot run for the trough and the equivalent rectangular tank of 
equal width, and the same will be true whether the major axis be 
horizontal or vertical— the advantage of the trough (as regards 
sheeting area) being equally lost whether the cross-section be very 
deep and narrow, or very broad and shallow. 

If the question be regarded from the common-sense point of 
view, it will be clear that the greatest economy of sheeting area, 
to contain a specified volume per foot run, would be obtained if 
the tank and trough were combined to form a semi-cylindrical trough. 
Hence, in selecting the proportions for a particular case, the 
endeavour should be to obtain a cross-section for the combined tank 
and trough which differs as little as possible from the equivalent 
semi-circle. 

Since there must be vertical side walls to form the supporting 
girders, even were the trough bottom semi-cylindrical the combined 
cross-section would differ from a semi-circle. Moreover, as has been 
stated already, to minimise bending actions in the curved plates 
under maximum head, the section of the trough should be semi- 
elliptical, with the major axis vertical, and therefore, a certain 
amount of divergence from the semi-circular cross-section is unavoid- 
able for practical reasons. This divergence should, however, be 
the minimum consistent with practical considerations, and deep, 
narrow troughs should not be employed unless the circumstances 
prevent the use of a more economical shape. The broad, shallow 
trough is, of course, objectionable by reason of its shape being 
unsuitable for the loading. 

A numerical example will provide the best means for obtaining 
some idea of the extent to which practicable cross-sections involve 
increased sheeting area as compared with the equivalent semi- 
circular sections. Take a width constant at 14 ft., and consider 
three different depths, the capacity of the trough being equal to 
that of the rectangular portion in each case. 

First, let ^ = 6 ft., so that 8 will be 6 x i'27 — 7-62 ft. This 

section is shown at {a) in Fig. 19. The total capacity will be 168 
F 



66 



TANK CONSTRUCTION 



cub. ft. per foot run, and the area of sheeting 12 + 22*97 = 34'97 
sq. ft. per foot run. A semi-cyhndrical trough to give the same 
capacity would be 20*69 ^t. in diameter, and its area of sheeting 
32*51 sq. ft. per foot run. Here the increase is 2*46 in 32*51, or 
about 7*6 per cent. The equivalent semi-circle is shown in the sketch 
for comparison. 

Second, let ^ = 7 ft., so that 8 will be 7 x 1*27 = 8*89 ft. This 
section is shown at (b) in Fig. 19. The total capacity will be 196 
cub. ft. per foot run, and the area of sheeting 14 + 24*97 = 38*97 
sq. ft. per foot run. A semi-cylindrical trough to give the same 




Fig. 19. 

capacity would be 22*35 ^t. in diameter, and its area of sheeting 
35*14 sq. ft. per foot run. The increase in this case is 3*83 in 35*14, 
or about 10*9 per cent. 

Third, let ^ = 8 ft., so that 3 will be 8 x 1*27 = 10*16 ft., as 
at (c) in Fig. 19. The total capacity will be 224 cub. ft. per foot 
run, and the area of sheeting 16 + 26*97 = 42*97 sq. ft. per foot run. 
A semi-cylindrical trough to give the same capacity would be 23*88 ft. 
in diameter, and its area of sheeting 37*5 sq. ft. per foot run. Here 
the increase is 5*47 in 37*5, or about 14*58 per cent. 

These increases are not all loss, however, for the semi-cylindrical 
trough taken as the standard of comparison would require supporting 
work in addition, probably costing much more than would the 



ECONOMY OF FORM 



67 



increases in sheeting area required for the more convenient 
rectangular tanks with trough bottoms. 

It would be the reverse of advantageous to put more of the 
capacity into the troughs for these cases, unless the breadth could 
be increased. A little consideration will show that, keeping the 
breadth unaltered, the trough would become deeper if its volume 
were increased, and the divergence from the equivalent semi-circular 
cross-section would be greater. Saving might be effected with the 
largest of the three if the capacity of the trough were made double 
that of the rectangular portion, the breadth being increased to 18 ft. 

224 



The depths would then be : d 



= 4-15 ft., and 8 = 4-15 X 




Fig. 20. 



3X 18 

2 X 1*27 = io'54 ft., giving the area of sheeting 8*3 -f 3071 = 39 
sq. ft. per foot run. This section is 
shown in Fig. 20. A semi-cylindrical 
trough to give the same capacity would 
be 23*88 ft. in diameter, and its area of 
sheeting 37*5 sq. ft. per foot run, so 
that the increase for the more con- 
venient form would be only 1*5 in 37*5, 
or about 4 per cent. — a very consider- 
able reduction from the I4'58 per cent, 
for the same capacity with the width 14 ft. and the trough equal 
in capacity to the rectangular portion. 

These results show clearly the advantage, as regards area of 
sheeting, of putting a large proportion of the capacity into the trough 
provided the breadth be sufficient to give a fair degree of approxi- 
mation to the equivalent semi-circular shape. 

For the shorter rectangular tank with a trough bottom^ — i. e. 
where the sheeting in the ends is not insignificant as compared with 
that in the sides^ — mathematical investigation is unnecessary. From 
the facts it follows obviously that the form giving greatest economy 
of sheeting area would be a hemispherical bowl, and the endeavour, 
in selecting proportions for a particular case, should be to depart 
as little as may be from the equivalent hemispherical bowl. 

26. General Considerations regarding Shaped Bottoms. — A few 
general points regarding curved or dished bottoms may be noticed 
in concluding this consideration as to economy of form. 



68 TANK CONSTRUCTION 

It has been shown that the curved form is economical as regards 
sheeting area, and also as regards support and stiffening. On the 
other hand, the costs of manufacture, transport, and erection are 
inevitably greater with curved than with fiat sheeting. It is, there- 
fore, quite possible (and has frequently happened) that a tank having 
a dished bottom may be lighter, and yet cost considerably more 
than would the plain flat-bottomed tank, with its supporting joists, 
to give equal storage capacity. 

No hard-and-fast rule can be laid down, of course, for circum- 
stances of locality and available labour must very largely influence 
particular cases, but it is probable that, for cylindrical tanks, flat 
bottoms with supporting joists are cheaper than dished bottoms 
for diameters less than 20 ft. In any case, economical manufacture 
for dished bottoms cannot be expected unless the diameter and shape 
have been adopted as stock, dies and forms for the shaping being 
already available. The plates for such a bottom cannot be properly 
shaped without forms, and even then they must be worked hot. 
Hence, if the diameter of the tank be selected without reference 
to forms which manufacturers may have available, it will be neces- 
sary to either make new forms or adapt existing ones, and the cost 
(charged, of course, to the one job in full) will be great, if not 
prohibitive. 

For rectangular tanks with trough bottoms, the advantages 
of the trough become effective for smaller widths than with cylin- 
drical tanks, because the bending and other work in connection 
with the plates for the trough is less costly than for the spherical 
or spheroidal dish. Probably the flat bottom with supporting 
joists will cease to be more economical in cost where the width is 
upwards of 12 ft. or 15 ft. 

Always, circumstances must influence the form selected. In 
perhaps the majority of cases in ordinary practice, economy in 
the tank itself is a secondary consideration, giving way to the demand 
for convenience or space utilisation, and then the best that can be 
done is to obtain the most economical design for a specified form 
and (more or less) imposed set of proportions. 

The matter of curved bottoms for tanks — in this country at 
least — is somewhat difficult from the commercial point -of view. 
There has not been sufficient demand for such work to induce manu- 



ECONOMY OF FORM 69 

facturers generally to adopt stock sizes and proportions and make 
the necessary forms and dies. On the other hand, so long as forms 
are not available, any tendency to create a demand is checked by 
the high costs of manufacture, and until these opposing considera- 
tions are reconciled it will be impossible to secure the full advantages 
possessed by dished and trough bottoms. 

An attitude which designers might well adopt is a constant 
readiness to use dished or trough bottoms for tanks where advantage 
may be obtained by so doing, coupled with an insistent and propor- 
tionate demand for conclusive evidence as to the reality of the advan- 
tage. This, of course, implies an intimate and accurate knowledge 
on the part of the designer, as to the costs of manufacture, transport, 
and erection of all classes of work, and the ability to judge correctly 
as to which methods are likely to be most economical in each indivi- 
dual case. It implies also an impartial view of all available methods, 
and not a hidebound preference for one form solely because it is 
easy to design, and without reference to its merits, both actual and 
relative. It might be well if designers were to consult manufacturers 
more than they do, before deciding on a particular form for a tank, 
so as to ascertain whether the work involved in a tentative design 
can be done at reasonable cost, or (as sometimes happens, and is 
undesirable from almost every point of view) is the exclusive 
speciality of one yard. 

We shall turn next to the design of tanks generally, as regards 
strength and stiffness, arrangement of plates, connections, methods 
of erection, and such matters. In later chapters, dished and trough 
bottoms are considered from these points of view. 



CHAPTER III 

FLOORS AND WALLS OF RECTANGULAR TANKS 

27. Tank Floors and Walls Generally. — The loading to which 
the walls and bottom of a tank are subjected is, in general, that due 
to the weight of the contained liquid. It is not often that the liquid 
is stored under pressure ; but even if it were, the ordinary gravita- 
tional loading would simply be increased by the amount of pressure 
imposed. 

It is commonly stated that the pressure per unit area at any 
level in a liquid acts in all directions, and is equal to the weight of 
the column of liquid which would stand upon the unit area, of height 
equal to the vertical distance between the upper surface of the hquid 
and the level in question. This is strictly true where the area under 
pressure is horizontal, but for a vertical or inclined surface it involves 
the contradiction that, since the intensity of pressure varies directly 
with the depth, the pressure cannot be uniform over a whole unit 
of area. For the purposes of practical design, however, it is 
sufficiently accurate to work as though the pressure intensity were 
constant over the whole area under consideration, its magnitude 
being taken as the greatest likely to act. 

Obviously, to design the walls of a tank thus causes a waste 
of material, for, since the loading varies with the depth, so also, 
to secure economy of material, should the strength of the sheeting. 
Plates of diminishing thickness are not easily obtainable, however, 
and would be costly to produce. The diminution in thickness for 
the wall of a rectangular tank would need to be parabolic to give 
uniform diminution in strength, since the resistance to bending 
of a plate varies as the square of its thickness. 

Where the tank is of considerable depth, saving may be effected 
by making the plates of each strake thinner than those of the strake 
immediately below, but the strakes are usually of the maximum 



FLOORS AND WALLS OF RECTANGULAR TANKS 7T 

width convenient to use. Each strake must be riveted to its neigh- 
bours, and the seams must be tight against leakage. Every strake 
used, then (after the first), means a horizontal seam all round the 
tank, and, as a rule, it is cheaper to avoid this riveting as much as 
possible, even at the expense of sheeting. Doubtless, if good riveting 
were less troublesome and costly to obtain, tanks might be designed 
more economically, in some cases, by the use of narrower strakes, 
but under ordinary circumstances in this country the main object 
is to minimise riveting. It must be remembered, also, that riveted 
seams take time to make and caulk properly, especially if the work 
must be done during erection at the site. For all ordinary widths, 
the price of mild-steel plates per ton is the same, and hence, against 
the saving which might be effected through frequent reductions 
in the thickness of the plating with narrow strakes, there must be 
set not only the cost of the riveted seams, but also the cost of the 
extra time required to make them. 

We will consider first the design of the tank bottom, returning 
to the side walls afterwards. 

28. Design of the Rectangular Flat Floors. — Where the tank 
bottom rests directly upon a solid base of concrete or other similar 
material, there is, of course, no need to design the plates for strength. 
The minimum thickness allowable (generally J in.) may then be 
used, and the riveting sufficient only to secure tightness of the seams 
against leakage. 

For a flat bottom supported on bearer- joists, the plating is, 
clearly, in the position of a beam, uniformly loaded. When cal- 
culating to find the thickness required, it is convenient to consider 
a strip of the plate i ft. in width, since all such strips are similarly 
loaded. 

Conflicting views are held and expressed as to what should be 
taken for the span of this beam. Some say the distance between 
the centres of the supporting joists; others the clear distance 
between the flanges of those joists; and others distances inter- 
mediate between these two. Others, again, contend that the plates 
will act as a continuous beam, with points of contraflexure between 
the supporting joists; and that the distance between these points 
of contraflexure should be taken as the span. 

In fact, the question depends largely upon circumstances. If 



72 TANK CONSTRUCTION 

the bottom were formed of a single plate, perfectly flat, and the 
supporting joists very narrow and stiff, with perfect bearing of 
the plates throughout, the conditions would be those of the con- 
tinuous beam. The points of maximum bending moment would 
then be over the supporting joists, however, and if the pitch of the 
joists were constant throughout the length of the tank, with a joist 
under each end wall, the bending moment in the plate at the joists 
next to those at the extreme ends would not be less than that for a 
freely supported beam-strip spanning from joist to joist. Hence, 
there would be no saving, for the plate must be throughout of the 
thickness required for the position of the maximum bending action. 
Of course, the end spans, and those next to them, could be made 
less than those towards the middle of the tank, and the bending 
moments thus kept more nearly equal throughout the length of the 
bottom ; but it will be clear that trouble and expense would be 
involved, reducing the advantage to be obtained. 

In actual tank work the conditions are (the author considers) 
not such that reliance could be placed upon the plates acting in 
accordance with the theory of continuous beams, though, of course, 
since the plates are continuous over the supports, there must be 
some such action. As the extent of the action cannot be estimated 
with any reasonable probability of truth, it is better that it be not 
calculated upon to any great extent. 

The argument for taking the span as the full distance between 
the centres of the bearer- joists is based upon the assumption that 
the flanges of the joists will bend easily when the load comes upon 
them, leaving the plate supported over the joist webs. This may 
be regarded as an unnecessarily severe assumption, though, of 
course, there is not much difference between the distance between 
the centres and that clear between the edges of the flanges in ordinar}^ 
cases. 

A little consideration will show that, having regard to the 
circumstances of material and workmanship in such structures, 
no definite theory of action can be laid down. The best that can 
be done, for the purposes of practical design, is to obtain a simple 
and convenient relation which may be reasonably depended upon 
to give safe results without avoidable waste of material. 

With regard to this question of necessary and minimum per- 



FLOORS AND WALLS OF RECTANGULAR TANKS 



73 



missible plate-thicknesses, it should always be remembered that 
the use of a slightly greater thickness than that of the absolutely 
irreducible minimum has the advantage of giving a longer life to 
the structure, as well as tending to reduce the liability to leakage 
through opening of the seams. There can be no justification for 
useless piling up of weight, but where a calculated thickness lies 
between two stock thicknesses, and the question arises whether 
the next below or the next above shall be used, it should not be 
forgotten that the advantage of the " cut " thickness is confined 
to first cost alone, whereas the stouter plate will most likely give 
better value in a greater degree of permanence. 

The method here suggested for design is to space the bearer- 
joists equally, leaving about one-third spaces overhanging at each 
end, as indicated in Fig. 21, and to design the plate as though its 




Fig. 21, 



span, both for loading and supporting, were the clear distance 
between the edges of the bearer-joist flanges, with ends freely 
supported. This, of course, is a compromise, for the actual con- 
ditions are probably not in accordance with the assumptions made ; 
but the thicknesses so found have proved reliable in practice. 

A simple expression for the thickness of the plate may be deduced 
on this basis, as follows — 

Taking the span L and the depth D (Fig. 22), both in feet, the 
load on a strip of plate i ft. in width will be (L x D X i) cub. ft. , 
at 62*5 lb. per cub. ft. if the liquid be water. Then, the load on 
the beam-strip of plate will be — 



W = (62-5 X L X D) lb. = 



62-5 X L X D 
2240 



tons; 



and the maximum bending moment will be — 



^ 12 W L 12 X 62-5 L2 D 75 L2 D . ^ 

B = — 5 — = — ^ = '- m.-tons. 

8 8 X 2240 1792 



74 



TANK CONSTRUCTION 



But B =/ X M, where /is the maximum permissible stress at the 



extreme fibre in the plate, and M is the section modulus = 



6* 



12 X i^ 
The value of M will be — . — = 2 /^ where t is the thickness in 

inches ; and taking /as 7-5 tons per square inch — 

75L2D 



whence — 



1792 



= 7-5 X 2^2^15/2; 



^2 _ 75L2D _ L2 D 

15 X 1792 358-4' 



and — 



1 ^ Suf 



>r Uicsi^iD -^ 



D 



Fig. 22. 



t = 



358-4 



18-9 • 



Now, this will seldom give a thickness an exact number of 
sixteenths of an inch, and hence, if we agree to take always the 
nearest sixteenth above the value found from it, the expression may 
be still further simplified to — 

lVd . . 

-^^ ...... .(32) 



t = 



A common spacing for the bearer-joists is 3 ft., centre to centre, 
and if the joists have flanges 3 in. in width, L will be 275. 



FLOORS AND WALLS OF RECTANGULAR TANKS 

Then, for a depth of 5 ft., 



75 



t = 



275 X V5 __ II X 2-236 _ 5-09 



20 



4 X 20 



16 



and the thickness should be | in. The same thickness will be 
sufficient for depths of 6 ft. and 7 ft., the comparatively small 
margin for the latter depth taking the thickness to y^ in. if any 
allowance be necessary to provide for corrosion. For a depth of 
8 ft. or 9 ft., the thickness should be yV ii^-' ^^^ ^^^ depths of 11 ft. 
or 12 ft., the thickness should be J in. This, of course, is on the 




Fig. 23. 

assumption that the plates hold the nominal thickness with reason- 
able uniformity throughout. If there be any reason to suppose 
that the actual thickness may be less in parts than the nominal 
thickness, a proper and corresponding allowance should be made 
in the thickness selected. 

To the thicknesses obtained from equation (32) must be added 
any allowance necessary to provide for corrosion, but in most 
cases — at least for plates J in. and over in thickness — the allowance 
for corrosion may start from the thickness obtained as the value 
of t from the equation. Thus, if the additional thickness to allow 
for corrosion is to be yV in., with L = 275 and D = 8 ft., the value 



76 TANK CONSTRUCTION 

6*226 

of / as found from the equation will be ^ , which is slightly 

under 6| sixteenths, and adding the yjV in. for corrosion, the thick- 
ness is still about -^\ in. less than y'g- in. The plate might, then, 
be made -f^ in. in thickness, for all but exceptional circumstances. 
Of course, all such points must be dealt with according to the 
particular circumstances and conditions of each individual case, 
a selection of thickness perfectly reasonable in one case being 
unjustifiable in another. 



Fig. 24. 

29. Seams in Flat Floors. — Where the length and breadth of the 
tank are such that seams are unavoidable, the plates should be so 
arranged that the seams will lie transversely to the bearer joists, 
as indicated in Fig. 23. By this means, the disturbance to the 
beam action of the plates, and hence the tendency to leakage 
through the opening of the joints, will be less than with the seams 
running parallel with the joists, as in Fig. 24. 

The rivet heads should be countersunk on the underside where 
the seams cross the supporting joists, so that the bearing may be 
as even as possible. 

The seams now under consideration are those connecting plates 
which run in one piece from end to end, or from side to side (which- 
ever may be the most convenient), of the tank bottom. They may 



FLOORS AND WALLS OF RECTANGULAR TANKS 77 

be conveniently termed '' main " seams, in contradistinction from 
the " subsidiary " seams which are necessary when the length of 
the strips is so great that a single plate would be impossible or 
impracticable. 

It is open to question whether lap or butt joints should be used 
for the main seams. The consensus of expressed opinion is in favour 
of the single-riveted lap joint, solely on the score of cheapness. 

Since tightness against leakage is the only condition to be 
satisfied in such seams, single riveting is sufficient for either type 
of joint, and from this it follows that the butt joint demands two 
rivets for every one required by the lap joint, while the butt with 
a single cover strip involves twice, and that with double cover 
strips three times, as many rivet holes as are necessary with the 
lap joint. 

There need be no extra edge-planing, however, with the butt 
joint, for the cover strips may be of stock flat bars, the edges of 
which seldom require planing to render them suitable for caulking. 
Even where lap joints are used, unless some special means are 
adopted at the mills to secure fair edges, it is only in the roughest 
and poorest work that the edges are allowed to go unplaned, for 
the relatively small saving effected by omitting the planing of bad 
edges is nearly always lost many times over, through the increased 
difficulty in caulking to render the seams tight, and the time thus 
wasted. There is, of course, more caulking (as regards length) 
to be done with butt joints than with lap joints, but, on the other 
hand, the caulking is much easier to do with the former, and more 
likely to be satisfactory, as the plates are better supported. 

A point in favour of butt joints for the main seams lies in the 
fact that they give the tank a flat bottom, and, consequently, a 
better bearing on the supporting joists. If single cover strips are 
used, they may be placed on the inside, and if double cover strips 
be preferred, those on the underside may be stopped just clear of 
the flanges of the supporting joists. 

With lap joints, the best arrangement is that indicated in Fig. 25, 
with packing strips to give the alternate plates a bearing upon 
the supporting joists. These packing strips should have the same 
width as, and be tacked to, the joist flanges. Two rivets to each 
strip are sufficient if the strips be reasonably straight and flat. If 



78 



TANK CONSTRUCTION 



the bearing joists are to act as continuous beams (which is the 
most economical plan), there will be the least possible reduction 
in the strength of the joists if the tacking rivets be placed one at 
each extremity of the middle half of the span — i. e. at a quarter 
of the span from each beam carrying the bearer joists, — for that 
is the neighbourhood of the points of contraflexure in the joist; 
or, of course, the tacking rivets will do no harm if they he w^ell 
within the middle half of such span, for there the upper flange of 
the bearer joist will be in compression. If the supporting joists 
are to act over separate and freely supported spans, the tacking 




Fig. 25. 

rivets should be placed as near the ends of those spans as is practic- 
able. The heads of the tacking rivets must be countersunk at the 
upper sides of the packing strips, of course. 

For shallow tanks, where the thinnest practicable plates (J in. 
being usually the minimum permissible thickness) for the bottom 
are stressed well below the allowable working stress, the packing 
strips of Fig. 25 may be dispensed with by altering the arrangement 
of the plates and seams. If the main seams lie parallel with the 
supporting joists, and the distance between adjacent seams be 
50 per cent, more than the pitch of the joists, the arrangement of 
Fig. 26 will cause the seams to be placed at or near points of contra- 
flexure in the bottom-plating. The joists which are to carry the 
raised plates of the bottom should be suitably packed from the 
main or secondary beams, as shown, the packing pieces being of 
the area comprised in the intersection of the two flanges, and of 
thickness equal to that of the bottom-plates. 



FLOORS AND WALLS OF RECTANGULAR TANKS 



79 



All things considered, and given the same class of work and 
standard of requirements for both, it is probable that lap joints 
for the main seams are cheaper than butt joints, but the difference 
in cost is not nearly so much as might appear from a cursory examina- 
tion. Moreover, in cases where a thoroughly sound job is regarded 
as of more consequence than a perhaps trifling reduction in first 




cost, and where the need for rapidity in installation demands that 
the time absorbed in trials and re-caulkings before the tank is 
ready for service shall be minimised, it is probable that the use of 
butt joints for the main seams can be justified from all points of 
view. 

When subsidiary seams in the bottom- 
plates are unavoidable, the object should 
be to place them where there is the least 
probability of their being opened so far 
as to permit leakage. With the arrange- 
ment of Fig. 23, such seams must, of 
course, lie perpendicular to the main 
seams, and, hence, parallel with the 
supporting joists. To subject a joint, 
whether of the lap or butt type, to a severe cross-bending action, 
as indicated in Fig. 27, must, obviously, tend to open the joint, 
and as the strength of such a joint to resist cross-bending would be 
practically impossible to estimate with any reasonable probability 
of truth, the endeavour should be to prevent the application of 
such actions. 

.It seems reasonable to suppose that if a subsidiary seam bo 




Fig. 27, 



8o 



TANK CONSTRUCTION 



placed at about one-fourth of the distance between the joist-centres 
from a supporting joist, as indicated in Fig. 28, the bending action 
upon it cannot be very severe, because of the effects of continuity. 

Subsidiary seams, it is here suggested, should always be butt 
joints, with double cover strips. Besides giving a seam less hkely 
to open, such a course is, as will be seen presently, of assistance in 
securing a convenient arrangement of the plating. 

Another method of deahng with the subsidiary seams is to stiffen 
the bottom-plates in the neighbourhood of such seams. The seam 
may be placed midway between the supporting joists, and three 




Fig. 28. 



stiffeners, of fairly stout angle section— say, 3 J in. X 3i in- X f in.— 
riveted to the bottom-plates, as shown in Fig. 29. Two of the 
angle stiffeners may be incorporated in the main seams at each 
side, and the third one placed across the centre of the subsidiary 
seam. It is best to attach these angles to the underside of the 
bottom-plates, thus allowing the inner cover strip of the subsidiary 
seam to pass from main seam to main seam, and to be well caulked, 
while the outer cover strip may be cut to fit between the angles 
and main seams, as shown in the sketch. The rivets securing the 
middle angle stiffener to the bottom-plates may be f in. or | in. 
diameter and 6 in. pitch. 



FLOORS AND WALLS OF RECTANGULAR TANKS 



8i 



Other methods will doubtless suggest themselves, and it is only 
necessary to remark that anything in the nature of a trimmer 
lying along the subsidiary seam is undesirable, since the effects of 
continuity in the plating might cause the most severe bending 
action to be applied over such a secondary support — i. e. in the 
seam itself — and thus defeat the very object in view. 

30. Riveting in Floor Seams. — Where lap joints are used through- 
out the tank bottom, a difficulty arises at the junction of a sub- 
sidiary with a main seam, owing to the interference of the third 
plate. If the plates were brought together without preparation 
for this difficulty, the conditions would be as indicated in Fig. 30 — 



-COVER STRIP 



^ COVER ; U 2,TR IPS 
SECTIONAL ELEVATJOr^- 



^SUBSIDIARY 




L"t;i+_-t.i:.±.t.+.± 
+|i-t- -^•-f"-^■ + + -H 



j'BEAI^E.K JOIST 




two of the plates either butting, as at (a) ; or separated by a space 
equal to the thickness of the middle plate, as at {h). 

The best known (and most widely adopted) method for over- 
coming this difficulty consists of arranging the plates as at (a) 
in Fig. 30, thinning out the corner of the middle plate to a feather 
edge, and bending that of the newcomer, as shown in Fig. 31. 
Provided the work be weU done, this method gives a satisfactory 
job. It is, however, somewhat costly, for the two plate corners 
must be worked by forging, and care is necessary to ensure that 
all the surfaces in contact shall lie truly flat, since any spring would 
be fatal to tightness of the joint against leakage. Plates of even 
comparatively small size are awkward to hold and handle, both 
for heating and working, and consequently the cost is high. Very 

G 



82 



TANK CONSTRUCTION 



careful caulking is required with this method, especially around 
the feathered edge of the thinned plate. 

Another method, indicated in Fig. 32, consists of bending the 
third plate only, and introducing a tapered packing-piece at the 
end of the middle plate. This reduces the number of plates to be 
forged, but the smithing on those which must be forged is more 
comphcated, and, as the tapered packing-pieces need to be carefully 
prepared in addition, it is probable that an impartial investigation 
as to costs would show little (if any) advantage for this method as 
compared with that of Fig. 31. Even more care in caulking is 



Z2Z. 



■ '''^ m\m^KK^^ r.^:.^ ^^--^--^-- f^] r<(^.^^^...^^.v..^^ ^ 



0| 
^1 



1^;^ -^ i 





Fig. 30. 

required here, for there is the additional straight joint where the 
packing butts against the edge of the middle plate. 

The author is strongly of opinion that the best method is to 
use a butt joint for the subsidiary seams, as suggested in pp. 76-81. 
A httle more weight is involved, and a few more rivets and holes, 
but^there is no forging of plate corners required. For a tank of 
reasonable magnitude, and in ordinarily good-class work, it is 
probable that, on the question of actual costs for labour and material 
directly involved, this method would compare very favourably 
with either of those described above, while it would almost certainly 
give a considerable saving in time at the site, for the processes of 
assembling and caulking would unquestionably be simplified. 

Yet another method is available. The plates may be arranged 



FLOORS AND WALLS OF RECTANGULAR TANKS 



83 



as at {b) in Fig. 30, with a space between the extremes, and this 
space may be filled with a plain, straight packing strip, of width 
equal to the lap of the plates for the seam. The arrangement is 
shown in Fig. 33, and if the treatment be confined to the subsidiary 
seams, the method may prove both satisfactory and cheap. As 
will be seen, it permits the use of single-riveted lap joints throughout. 
Two disadvantages — perhaps not very serious ones — of this method 
are : (i) The increased irregularity of the tank bottom, requiring 
more packings to give the plates a working seat upon the supporting 



7ZZZZZ 



E 



& 



SSSSS3SSS 



3 





\rC 



Fig. 31. 



Fig. 32. 



joists ; and (2) the increased tendency towards weakness in the 
seam for resisting the cross-bending actions which may be applied 
to it. 

With regard to the question of economical spacing for the 
supporting joists, in so far as it affects the thickness of the bottom 
plates, it will be clear that there are two opposing considerations. 
For economy in the plates of the bottom, it is desirable that the 
supporting joists be as close together as possible ; and for economy 
in the joists themselves, they should, obviously, be as far apart as 
possible. The question is evidently affected also by the spacing 
of the beams which carry the supporting joists, for that determines 
•the span of those joists. 



84 



TANK CONSTRUCTION 



31. Attachment of Walls to Rectangular Tank Floors. — There 
are two principal methods in more or less common use for con- 
necting the wall plates to the floors of rectangular tanks. One is 
by means of angle bars, as indicated at (a) in Fig. 34 ; and the other 
is by flanging the bottom plates, as at {h) in the same sketch. 

The former method becomes troublesome if the main seams are 











>■ ' ' .r .f- I 1 VV y y / / y / / 



Fig. 33. 

formed of lap joints, for there is a space between the angle and 
alternate plates, as shown in Fig. 35. Packing strips might be 
used to fill these spaces, but such devices are often regarded un- 
favourably, and consequently the angle bar connection is used mostly 





y///yyyy.yyyd 



Fig. 



34- 



where the plates are thin, and can easily be drawn down at the 
corners to fit closely against the angles. 

Clearly, if the seams in the walls and bottom be of the butt 
type, the angle bar connection becomes very simple and convenient, 
for the plates will all he flat against the angle flanges, and the 
inner cover strips may be stopped close against the edges of the 
angles. 

The second method — as at (6) in Fig. 34 — is frequently used. 



FLOORS AND WALLS OF RECTANGULAR TANKS 



85 



By means of suitable dies and forms, the flanging of the plates may 
be done well and cheaply, though the plates must, of course, be 
properly heated first. This method, also, becomes very simple 
and convenient if all seams in the walls and floor of the tank be 
of the butt type. With lap joints it is necessary to provide for the 
interference of the third plate at the junctions of seams, and this 
is usually done by thinning down the corner of the middle plate. 




I 



:nr:<?=^^y?;^^^^ v^v^^^^V'.^^.^s^^.^vvv^^t<^<<<«;^^''''^•^''^^'^^^^ 



Fig. 35. 



The seams in the walls should be placed midway between those 
in the floor, and the arrangement will then be as shown in Fig. 36. 
Here, again, it is probable that the better method is to use 
packing strips for the alternate spaces so as to avoid the heating 
and forging of the plates at the corners otherwise necessary ; thin- 




FlG. 36. 

ning down the flanged corner of a bottom plate is particularly 
troublesome, and a troublesome operation is, almost invariably, 
costly also. 

With the second method the plates at the ends of the bottom 
must be flanged along two edges, and the corner made spherical, 
as indicated in Fig. 37. Also, the plates forming the corners of the 
walls must be bent to connect with the bottom, as shown. This 
needs to be very carefully done, and requires specially suitable 
appliances; but, on the other hand, such a corner needs little 



86 



TANK CONSTRUCTION 



caulking, and this saving should be taken into account when com- 
paring the cost with that of a corner connection formed by means 
of an angle bar. 

To minimise the necessary forms and dies for flanging and 
bending the plates, it is well to use a stock radius — about 6 in. 
is convenient for most cases — for all tanks, regardless of size and 
plate thicknesses. Provision should be made for the difference 
in radius where one plate lies inside or outside another, and this 
may be dpne by inserting packing strips between the dies and 
forms. A complete set of such packings should be kept, and 
regarded as part of the flanging apparatus. They may be made 
from strips of ordinary stock plates, of suitable widths 
and lengths, and in all the usual working thicknesses. 
The dies and forms must be made with sufficient 
difference in radius to accommodate the packing 
strips, of course. This may seem rather in the 
nature of a refinement ; but it will be found that a 
little trouble and care taken in preparation, to ensure 
that the pieces shall all come together properly when 
assembled, is nearly always a sound investment. 

32. Cantilevered Walls of Rectangular Tanks. — If 
the side walls of a rectangular tank were not stayed 
or braced in any way, they would be, in effect, 
simple retaining walls, and would have to possess, 
through their own mass, adequate resistance to 
movement and overturning. There are, of course, tanks — or, at 
least, structures which fulfil the purposes of tanks — for which the 
side walls can only be designed and constructed on this basis, but 
such types do not lie within the scope of this work. ]\Iodifications 
of the retaining-wall principle may, however, be applied sometimes 
with advantage, as will be shown presently. 

For tanks constructed of steel sheeting, or of such materials as 
reinforced concrete, the side walls almost invariably require to be 
stayed or braced in some way; and as the design of the sheeting 
or panelling depends to a large extent upon the disposition and 
effects of the staying, it will be well to consider the various ways 
in which the walls may be stayed, having regard to their influences 
upon the economy of sheeting or panelling. 




Fig. 37. 



FLOORS AND WALLS OF RECTANGUIAR TANKS 87 

Before proceeding to this, however, we may consider one case 
in which no special bracing {i. e. no additional ties or framing) 
need be provided for supporting the side walls, the only requisite 
being that the walls shall be connected to the floor with adequate 
strength, stability, and stiffness. This case is the shallow tank 
which forms the dished floor and collector for an elevated cooling 
tower, such as is used for cooling the circulating water for the 
condensers working in connection with steam turbines. Instances 
of this type of tank occur also in other circumstances where large 
horizontal area is either unavoidable or more desirable than strict 
economy of form. 

Such tanks are usually about 2 ft. to 3 ft. in depth, and may 
be conveniently constructed of steel plates. A suitable and common 
arrangement for the plating is indicated in Fig. 38, the plates being 
preferably connected by means of single-riveted lap joints for the 
main seams, and single-riveted, double-covered butt joints for 
the subsidiary seams. If a curb is required around the brim of the 
tank, it may be of light angle section, with flat bar packings to the 
alternate plates, which will be recessed by reason of the lap seams. 
The riveting for the curb need be only so much as is required for 
the purpose, and it is clear that tightness against leakage can 
scarcely be an important condition for such riveting. 

In such tanks as that illustrated in Fig. 38, the side walls stand 
as cantilevers, and the stresses in the plates should be estimated on 
this basis. Since each section of the side walls is in one piece 
with the corresponding bottom plate, it follows that there is a 
maximum permissible depth or head of the contained liquid for 
each thickness of plate if the maximum permissible working stress 
in the material is to hold as far as possible throughout the structure. 

We will investigate the conditions as to the effective length 
and loading of the cantilever portions, and determine the maximum 
allowable heads for each plate thickness in common use. 

Clearly, the conditions for the end walls will be somewhat 
different from those for the side walls, since the bearer joists lie 
transversely to the former and parallel with the latter. We shall 
return to this point presently, and examine the difference and its 
practical effects upon the design. 

Let us consider the end walls, with the bearer joists running 



88 



TANK CONSTRUCTION 



transversely. An enlarged section of the parts concerned is shown 
for clearness in Fig. 39, with the bearer joists indicated by dotted 
lines. For simplicity in the investigation, we will confine our 
attention to a strip of the wall i ft. in length. 

The maximum bending moment will occur at the section A A, 



v^ 



r 



f 



I I 

— SECTIONAL ELEVATION. 



T 



I 



J 




PLAN — 
Fig. 38. 

where the bottom plates lose the support of the bearer joists, and 
the arm of the cantilever should be taken, rather full than short, 
as the distance (indicated as L in Fig. 39) between the section A A 
and the surface of the liquid, measured along the plate. 

To determine precisely the variations of loading and stress for 
the cantilever strip under a given head of the contained liquid might 
be interesting as an exercise, but would occupy more time than 
could usually be spared in commercial offices. The diagram of 



FLOORS AND WALLS OF RECTANGULAR TANKS 



89 



loading would be somewhat as indicated at (a) in Fig. 40, and the 
correct load diagram for a given head might easily be plotted; 
but the bending moment would obviously be troublesome to calcu- 
late. Moreover, since the head and density of the contained liquid 
are neither constant nor accurately known, and the plates must be 
in stock thicknesses, no useful purpose would be served by employ- 
ing such refinements in calculation. It is much easier, and quite 
as rehable for practical purposes, to take the effective head as 
equal to the cantilever arm, and to work on this as though the 
intensity of loading were simply proportional to the distance along 



f \ 





— ■■ — j< 


L 




1 1 1 
— I 


\ 


k 


>r 




Fig. 39. Fig. 40. 

the cantilever arm measured from the surface of the liquid, as 

indicated at (6) in Fig. 40. 

If the arm of the cantilever be represented by L (measured in 

L w 
feet), the average intensity of loading will be pounds per square 

foot, where w is the weight of the liquid in pounds per cubic foot. 
For water, w may be taken as 62 lb., giving the average intensity 
of pressure as 31 (L) lb. per sq. ft. The total load on the cantilever 
strip will be 31 (L^) lb., and the resultant pressure will act at a 
leverage of J (12 L) in. = 4 L in. from the section A A. Hence, 
the bending moment at A A will be — ■ 

B = 31 (L2) X 4 (L) = 124 (U) in.-lb. 
124 



2240 ^ ^ 3 



1^ (U) in.-tons. 



90 



TANK CONSTRUCTION 



If / represents the plate thickness in inches, the section modulus 
of the strip will be — 

M = I (i2 i^) = 2 t^ in. -units ; 

and with a permissible maximum stress of 7*5 tons per sq. in. in 
the material, the resistance moment will be — 

R = 7*5 X 2 ^2 ^ J- 12 in. -tons. 



Hence — 
and 



^1^ (U) = i5i'; or, U = ^^ J-5- it') = 271 t\ 
L = {^^jUf) } = 6-4713 } ^7^} ft. 



Inserting appropriate stock values for t, the following table may 
be constructed : — 



O t/1 
{/I -S 

c c 

.a c 

.a— ' 
II i2 



TTT 



7 
T6 



Txr 



I 



Calculations. 



L = 


= 6-4713 (\/ ,5) 


L = 


= 6-4713 (V^,'3'6) 


L = 


= 6-4713 (\/ 6^4 ) 


L = 


-•47x3 (x/^^) 


L = 


= 6-4713 (v ^ ) 


L = 


= 6-4713 (\7,36) 


L - 


-•47.3 (^f[) 


L = 


/ s/i2I\ 

= 6-4713 (V ,56) 


L = 


= 6-4713 (v/.'e) 



6l4_7L3 
2-5198 

6-4713 X 2 -9240 

6-3496 

6-4713x2-0801 

4 

6-4713x3-6593 - 
6-3496 

6-4713 
1-5874 
6-4713X4-3267 

6-3496 
6-4713X2-9240 

4 
6-4713X4-9461 

6-3496 
6-4713X2-0801 

2-5198 



L = Length of 

Cantilever Arm, 

in Feet. 


H = Maximum 

Permissible Head 

in Feet. 


2-57 


2-28 


2-98 


2-69 


3-36 


3-07 


3-73 


3*44 


4-08 


3-79 


[ 4-41 


4-12 


' 473 


4*44 


1 

5-04 


4*75 


5-35 


5-06 



In determining the maximum permissible depth or head, it must 
be remembered that L is to be measured along the flanged plate. 



FLOORS AND WALLS OF RECTANGULAR TANKS 



9^ 



If the flanging is 6 in. radius, as shown, the quadrant length will 



be 



2 X 6 X 3*1416 
4 



= 9-42 in. = 079 ft., so that, as the arm of 



the cantilever strip gains 079 ft. while the actual depth gains only 
0*5 ft., the calculated values for L should be reduced by 0*29 ft. 
(i. e. the excess of 079 ft. over 0-5 ft.) to give the maximum per- 
missible heads (H in Fig. 39) as in the last column of the accom- 
panying table. 

Returning to the side walls, lying parallel with the bearer joists, 
it will be clear that the bending moment in the plating depends 
upon the spacing of the bearer joists. The object, for all-round 
economy and suitability, should be to so arrange that the maximum 
bending moment from the cantilever portion occurs at the section 
where the bottom plate leaves the horizontal and commences its 
upward curve, since that is the condition in the end walls. 




h-L 



T 



jL^ 




T 



L -M 



Fig. 41. 



Although, as has been shown, it is not much use to apply 
elaborate continuous girder theory in the design of tank floors, 
some degree of approximation to the truth may certainly be obtained 
by taking account of the reasonable probabilities. In this case, 
if the side walls were turned down into the plane of the floor, and 
loading applied throughout to produce everywhere effects similar 
to those of the contained liquid in the tank, the conditions would 
be as indicated in Fig. 41. Then, regarding the plate as a con- 
tinuous beam, and assuming constant moment of inertia, with all 
supports at one level and of uniform rigidity, the stresses could be 
determined. 

The bending moment will attain maximum values at those 

sections where the slope of the plate-beam is zero, and it is clear 

that the most economical arrangement will be that which gives 

zero slope at all supports, including the extremes. This condition 

W S 
corresponds to a bending moment of at each support, W 



92 TANK CONSTRUCTION 

being the total load on each span, and S the length of each span. 
Considering a strip i ft. in width, as before, H and S being measured 
in feet, we have W = ze- H S = 62 H S for water. The bending 
moment at each support will be — 

T3 62 H S X 12 S /; TT C2 • n 

B = ^ 52 H 52 m.-lb. 

12 

Equating this with the bending moment from the cantilever strip — 

62HS2 = 124 L3; 

and if H be regarded as sensibly equal (for the present purpose) 
to L— 

S^ = 2 L^, whence S = i'4i4 L. 

To allow for the fact that L is, in reality, slightly more than H, 
and for convenience in design, we may take S = i"5 L. 

A design based on these proportions will be dependably sound 
provided that care be taken to ensure that the " assumptions shall 
be fulfilled so far as may be reasonably practicable. The bearer 
joists must be sensibly straight, and of uniform section ; the plates 
must be fiat all over the floor; and the bearer joists must be made 
to give proper support to the floor plates everywhere by means of 
packings. 

The end wall plates should return into each side wall, as shown 
in Fig. 38. They should also form an " outer " section, lying beneath 
the adjacent floor plates at the main seams. By this means they 
will be " tailed down " against the overturning effects of the canti- 
leverage through the weight of the contained liquid on the adjacent 
plates, and without subjecting the rivets of the seam to lifting 
tension — as might happen if the end-plates formed an ''inner" 
section. 

If vertical seams are necessary in the end wall plates, corre- 
sponding with the subsidiary seams in the floor plates, they should 
be of the same type as the subsidiary seams — that is, preferably, 
of single-riveted, double-covered butt joints. The outer cover 
may, of course, be stopped at the curb angle, and the inner cover 
at the lap of the first main seam. 



CHAPTER IV 

WALLS OF RECTANGULAR TANKS 

33. Stayed Walls of Rectangular Tanks. — We will now consider 
the various ways in which the side walls of rectangular tanks may 
be stayed against the outward pressure of the contained liquid in 
cases where they cannot be provided with adequate stability by any 
other suitable means. 

Many unintelligent and ineffective methods of staying are in 
use ; several others, reasonably sound in principle, are frequently 
so misapplied as to become worse than useless ; and yet others, 
though obviously simple and practicable, are altogether ignored. 
It will, therefore, be more expeditious and satisfactory to first 
examine the facts as regards conditions and requirements, rather 
than to discuss the different methods in turn. With the latter 
course, we could only compare the various methods with each 
other, whereas by examining the facts we shall obtain a basis, or 
standard, to which we may then refer each method for comparison. 
The merits and demerits of the various methods will thus be in 
no way subject to personal opinion, but will stand out clearly as 
facts — any particular method being good (or the reverse) according 
as it meets (or does not meet) the conditions and fulfils the require- 
ments, in a satisfactory manner for a reasonable cost. 

The loading to be resisted is, primarily, the horizontal outward 
pressure of the contained liquid against the vertical wall. Some- 
times (as will be seen presently) there are other additional factors 
in the loading, but these we may leave for treatment in due course. 
The intensity of the pressure in a liquid being directly proportional 
to the depth below the surface, it follows that the intensity of the 
pressure upon a side wall of a tank varies uniformly from zero at 
the surface of the liquid to a maximum at the base of the wall, 

93 



94 



TANK CONSTRUCTION 



^. 



Resultant 
pressure 



the resultant pressure upon a strip of the wall bounded by two 
cross-sections acting at a height (measured from the base of the 
wall) equal to one-third of the liquid head above the base. Under 
the action of varying heads, therefore, even were the density of the 
liquid constant, the loading on the side walls will vary both in 
magnitude and disposition. The magnitude and influences of the 
loading for a given head of a particular liquid may, of course, be 
readily estimated ; and in actual structures it is necessary to provide 
for the most severe conditions likely to arise. 

To resist this loading we have a vertical wall, which may possess 
either : (i) No dependable stability of its own to resist overturning ; 

(2) some degree of partial stability ; or (3) 
sufficient stability without assistance from 
stays or bracing. 

Of these three cases, the third was 
described and investigated in pp. 86-92 
(Chapter III), so we have the first and 
second cases left for consideration, these 
comprising, perhaps, the bulk of ordinary 
practice. 

For the moment we shall assume that 
the side wall is in all cases connected 
with the tank floor in such manner, as to 
prevent horizontal movement at the foot 
of the wall. Presently it will be shown that, in some circum- 
stances, such connection is scarcely required for stability, though 
it is, of course, always necessary to prevent leakage. 

In the first case, then, the conditions are as shown in Fig. 42, 
and it is obvious that, unless some additional resistance be pro- 
vided, the wall will be overturned by the action of the unbalanced 
outward thrust. These conditions are practically realised in the 
case of an ordinary rectangular steel tank having plane walls con- 
nected to a plane floor by means of angle bars, as indicated at [a) 
in Fig. 34. 

34. Staying by means of Top Curb. — The necessary additional 
resistance to overturning could be provided at the brim, by means 
of a curb possessing adequate strength against bending in the 
horizontal plane, as shown at (a) in Fig. 43, and this method might 




Fig. 42. 



WALLS OF RECTANGULAR TANKS 



95 



with advantage be more widely employed than it is. A curb is 
almost invariably provided for some purpose — even if only to form 
a " finish " — and it may be turned to useful account. For a small 
increase in the cost of the actual curb, real advantage could often 
be secured, giving appreciable saving in the cost of the side walls. 
Lateral deflection of the curb, within reasonable limits, will not 
adversely affect the stability of the wall. 

Each vertical strip of the w^all sheeting may then be regarded 
as a beam, freely supported at the ends, and carrying a load which 
varies uniformly in intensity from zero at some point in the span 
to a maximum at one of the supports, as indicated at (b) in Fig. 43. 




Fig. 43. 



If H be the head or depth of the contained liquid in feet, the 
maximum intensity of the pressure will be w H lb. per sq. ft., w 
being the weight of the liquid in pound per cubic foot. 

Considering a vertical strip of wall i ft. in width, the average 

w H 
intensity of pressure wdll be - — lb. per foot of height, and the 



total resultant pressure on the strip will be — 



F = 



X H 



lb. 



The reaction at the curb will be — 

r. ^ p{(H)/,„ + », ) = ^{ 



H 



\ _ wR^ 



3(H+.A)j 6(H + //)' 



96 TANK CONSTRUCTION 

and the reaction at the floor of the tank — 

R,=p{(f+-.)/iH+")}=-?(it|)=*(^'> 

w x^ 
The hquid pressure on a strip AB, x ft. in length, being lb., 

the bending moment in the strip at any section B distant x ft. 
below the surface of the liquid will be — 

B3 = |Rc {h + X) - — (y j) = \-^( H+xj e^ + ^) - — I 

-6\(H + A) "=]• 

For the conditions as indicated at (6) in Fig. 43, the bending moment 
diagram will be somewhat as shown at (c) in the same illustration. 

To determine the greatest bending moment in the strip, the 
easiest course is first to locate the section at which maximum 
bending moment must occur — i. e. the section at which the transverse 
shear is zero. Let this section be at M, distant x^ ft. below the 

surface of the liquid. Then, the liquid pressure on A M = — - , and 
for zero shear — 



2 ^^'^ ~ 6 VH + h)' 

whence — 

_ H3 



x^^ = .-.-., and X, = Vj(im) = ^'577 {V( im)}- 



The maximum bending moment (at ^I) will thus be — 

^"- - l^c [It + X,) - ~^[;j)] - \-6"(ir+A) 6~j 

= / ^ H^ (/? + a;o) - z£^ V (H + h) \ 
~\ 6 (H + A) j 

As a rule, it is well to provide for the possibility that the tank 
may be filled to the brim, in which case h = 0. Then the reactions 
will be — 

Kc = ^ ; and Rj. = . 



WALLS OF RECTANGULAR TANKS 97 

The depth of the section M will be — ■ 



^0= ^(^)== 0-577 H; 
the bending moment at any section B will be — ■ 

and the maximum bending moment (at M) — • 

_ w n^x^-w x\ H _ unc^ ,2 y 2\ 

-L>niax — ^ TT 6 '^0 /' 

which, on inserting the value of Xq (= 0-577H) becomes — 

-r, 0-577 Z£^ H / 2 H^ \ ^ TT^ 

If the contained liquid be water, or other liquid of equal density, 
w may be taken as 62 lb. per cub. ft., and the maximum bending 
moment will then be — 

B„.ax = 0-064 X 62 H3 = 3-977 H3, 

which, for all practical purposes, may be taken as — 

B_ = 4 H3 ft.-lb. = ^ ^' ^ ^^ = ^^ in.-tons. 
""^^ ^ 2240 140 

With plate thickness t (in inches), the section modulus of a strip 
I ft. in width will be : J x 12 x /^ = 2t^, and taking a maximum 
permissible working stress of 7*5 tons per sq. in., the resistance 
moment of the strip will be : 2t^ x 7-5 = 15/^ in.-tons. 

Equating the resistance moment with the maximum bending 
moment — 

15/2 — i> . whence t^ = — , 

^ 140 700 

and / = /-M" = :^' 3=. 0-0378 VW). 

\ 700 26-45 ^^ ^ ^ 

Also, by transposition — 

H3 = 700 /2; whence H = ^ 700 t^ = 8-879 (^1^ 
Inserting appropriate stock values for t, the following table. 

H 



98 



TANK CONSTRUCTION 



comparable with that given on page 90 for the wall strip flanged 
in one piece with the floor, may be constructed — 



t = 

Thickness 

of Plate 

in Inches. 


Calculations. 


H = 

Maxiniunn 

Permissible 

Head in Feet. 


1 
9 

f 

1 1 

T'li' 

1 


^y7oo 8-8790 
> 16 ~ 2-5198 


3-52 
4-09 
4-62 
5-12 

5'59 
6-05 

6-49 

6-92 

733 


^ _ ^700 X 25 25-9625 

V 256 ~ 6-3496 
. ^700 X 9 18-4689 

''-^64 - 4 

jj //700 X 49 32-4911 

V 2-56 6-3496 

3/700 :,, 

H - V ' ^ - J 175 - 5-593 

s /700 X 81 38-4174 

V 256 6-3496 

3/700 X 25 25-9625 

V 64 4 


^ _ //700 X 121 _ 43-9166 
^ 256 6-3496" 
•.5/700 X 9 18-4689 
" '^' 16 ~ 2-5198 



Comparing these depths with those tabulated on page 90, it 
will be seen that the permissible depth for each plate thickness is 
about 50 per cent, more with the arrangement here discussed than 
with the flanged wall arrangement of Figs. 38 and 39. 

In an actual tank the wall is subjected to the pressure of the 
liquid from the top of the angle bar only, as indicated in Fig. 44, 
the angle bar being amply sufficient to take the liquid pressure 
acting upon its upstanding limb in addition to providing the reaction 
for the base of the wall. Moreover, being riveted to the angle bar, 
the wall plate will be rather more favourably placed for resisting 
the bending action than we have calculated upon, owing to the lower 
•end having some slight (though not practically determinate) degree 
of partial fixity instead of being freely supported as we have 
assumed. 

Advantage may be taken of these facts, where desirable, by 



WALLS OF RECTANGULAR TANKS 



99 



RtSSURE 



ON Wall 



adding to the tabulated permissible depths the height of the up- 
standing hmb of the angle bar which connects the wall to the floor, 
to obtain the total permissible height from the floor of the tank 
to the brim. Indeed, where the circumstances are positively known 
to be favourable, an even larger concession may be made, the 
tabulated depths being increased by such a distance more than 
the limb of the angle bar as may be properly and truly justifiable, 
having regard to the facts, to allow for the slight fixity of the plate 
at its lower end. These matters are best left to the discretion of 
competent and responsible designers, for application according to 
the facts and circumstances of particular cases. Any attempt at 
generalisation must inevitably be liable 
to prove misleading, since the calcula- 
tions would be based upon assumptions 
which could not be equally realised in all 
cases. It will, of course, be clear that, 
even in the most favourable circum- 
stances, the permissible addition to the 
tabulated depth will seldom be more than 
an inch or two beyond the height of the 
upstanding limb of the angle bar; the 
object in referring to it here is to show 
that, in cases where the tabulated depth 
corresponding to a convenient plate thick- 
ness gives a capacity so slightly less than that required that a few 
inches of additional depth would suffice to make up the deficiency, 
it may be possible to justify the use of the convenient plate thickness, 
and thus to avoid increasing the cost of the tank walls, either b}- 
adopting the next greater stock thickness for the plates throughout, 
or by providing additional staying or bracing. 

The necessary transverse support at the brim may be provided 
either by making the curb itself sufficiently strong to span from end 
to end of the tank, or by using a lighter curb in conjunction with 
some convenient and effective form of trussing, staying, or bracing. 
Simple and economical methods for dealing with this point are 
discussed and illustrated in Chapter V, the same methods being 
suitable, with no more than slight modification and adaptation, for 
use with several distinct forms of wall support. 




Fig. 44. 



100 



TANK CONSTRUCTION 



One objection to the arrangement discussed above should be 
mentioned in passing. A more or less considerable direct tension 
is applied to the rivets which connect the wall plates to the floor 
angle bar, and it is always undesirable that tension should be 
apphed to rivets, more particularly where the rivets are required 
to maintain tightness against leakage of a liquid or gas. It is not 
a serious objection, for in spite of the enormous numbers of tanks 
which are constructed in this way, one never hears of even isolated 
cases in which trouble has arisen from this cause. It will be clear, 
however, that in some circumstances such tension might be at 
least undesirable, and we shall next proceed to show other methods 

of supporting tank walls against 
horizontal pressure, with which ten- 
sion in the rivets is minimised to the 
point of practical elimination, 

35. — Staying by Horizontal Rails. 
The necessary additional resistance 
to overturning of the wall might be 
provided at any other level, instead 
of at the brim. An instance of this 
is shown at (a) in Fig. 45, the upper 
support being there placed at the 
level of the resultant pressure when 
the tank is full to the brim. It 
may be thought that with this ar- 
rangement there would be no tension in the rivets connecting the 
wall plates with the floor angle, but such is not the case. By 
reason of its elasticity, the wall plating will deflect under loading ; 
and the supporting rail C, no matter how stiff and strong it be, 
will deflect also. In consequence, the elastic line of the wall plates 
under pressure will be somewhat as indicated at {b) in Fig. 45, and 
some tension upon the base rivets is clearly inevitable with the rail 
C at the level shown, or in any higher position. By fixing the rail at 
a lower level, tension in the rivets could be prevented, and by 
lowering the rail still further, the wall plate could be made actually 
to press inwards against the floor curb angle — with the tank full 
to the brim. The conditions would be altered, however, as soon 
as the surface of the liquid fell below the brim of the tank. 

With a rail giving support to the wall at some level between the 




Fig. 45. 



WALLS OF RECTANGULAR TANKS 



lOI 



floor and brim, as indicated in Fig. 45, the sheeting is better stayed 
than in either of the arrangements previously discussed. Con- 
sequently, for the same plate thickness, a greater head is permissible 
with this method of staying ; or, for a given depth of contained liquid, 
sheeting of less thickness may be used. 

The case merits a complete and general investigation, so that 
full advantage may be taken of the benefits offered. Such an 
investigation will be given presently, together with the inferences 
which may be drawn for convenience in practical designing; but, 
for the sake of clearness and simplicity, it may be well to consider 
first a typical instance having specified particulars. 




Fig. 46. 

Let the depth be 6 ft., with the rail C at a height of 2 ft. 6 in. 
above the base of the wall, as indicated at (a) in Fig. 46, the contained 
liquid being water. We shall regard the wall as hinged — i. e. fixed 
in position, but not restrained as to direction — at B, and calculate 
for I ft. run of wall, assuming the wall plate to be in one piece, and of 
uniform thickness, from top to bottom. 

The total liquid pressure on a i ft. strip will be — 

WH^ 62*6 X 36 r^^ / X It, 

= ^ = 1119-6 lb., or (say) 1120 lb. 



Taking moments about B, the outward force acting upon the 
rail C (per foot-run) will be — 

1120 X 2 



R. 



2'.^ 



= 8q6 lb.. 



leaving Rh = 1120 — 896 = 224 lb. per foot-run. 



102 TANK CONSTRUCTION 

In the portion A C, the bending moment at any section P^, 
distant x^ from A, nmy be found thus — 
Total pressure acting 

"W X 

= ft. -lb. (a;i being in feet), 

X 

Leverage of resultant = — ft. 

.-. Bi = — ^i = ^3:yl = 10-368 x^^ ft.-lb. 

This, clearly, reaches a maximum at C, where its magnitude will 
be— 

Bi^ax. = 10-368 X (3-5)3 ^ To-368 X 42-875 = 444-52 ft.-lb. 

444-52 X 12 o • - 

_ -TT-T u _ 2-o8 in. -tons. 

2240 

In the portion B C the bending moment at any section Pg, 
distant X2 from A, will be — 

B2 = {10-368 V — Re (^2 — A C)! = (10-368 x^^ — 896 (x^ — 3-5)} 
= (10-368 x^^ - 896 x^ + 3136) ft.-lb. 

Differentiating B2 with respect to x^ — • 

and for maximum bending moment, -^ — - = 0. 

CV Xn 

Hence, maximum bending moment occurs where 31 -i X2^ = 896, 
and denoting this particular value of %2 by Xq, we have — 

Xq^ = "^; = 28-8, and Xq = '\/28-8 = 5-37 ft. 

Inserting this value of x^ in the expression for the bending moment 
between B and C — 

B2,„ax. = 110-368 X (5-37)'! - 1896 (5-37 - 3-5) [ 
= (10-368 X 154-854) - (896 X 1-87) = 1605-53 - 1675-53 

r^ n 70 X 12 . ^ 

= — 70 ft.-lb. = — ^' = — 0-375 in. -ton. 

' 2240 ^'^ 

The magnitude of this bending moment is less than that at C, 



I 



WALLS OF RECTANGULAR TANKS 



103 



and hence, working on the latter, with the resistance moment = 15 
/^ in. -tons, as before — 

v2 _ 2-38 



15 



= o*i6, whence t = Vo'iG = 0*4 i 



m. 



With this arrangement, therefore, y^- in. plates would be sufficient 
tor a depth of 6 ft., as compared with 5*12 ft. for a curb at the brim 
(see page 98), and 3*44 ft. with the flanged plate arrangement of 
Fig. 38 (see page 90). 

The diagram of bending moments on the plate is shown at {h) 
in Fig. 46, there being a point of contraflexure between the rail C 
and the base of the wall. 

Now, it will be clear that if the rail C were lowered, the bending 




Fig. 47. 

moment at C would be increased, and that between B and C dimin- 
ished, giving a still greater disparity. On the other hand, if the 
rail C were raised, the maximum bending moments would become 
more and more nearly equal until, with the rail above a certain 
level, the maximum bending moment between B and C would 
preponderate over that at C. Obviously, the most economical 
arrangement will be that in which the bending moment at C is 
equal to the greatest bending moment occurring in the range B C, 
and to locate the position of the rail to give this, a general treatment 
is necessary, a convenient line of argument being as follows — 

With the conditions as indicated in Fig. 47, for no bending 
moment at B, the pressure upon the rail C (per foot-run) — 

_ _wW 

~ ^ '^ ~ 6 d' 



104 TANK CONSTRUCTION 

Let ^ = K H, then— 

^~6KH~ 6K' 

The bending moment at C will be — 

^ _ w (A C)3 _ wJR - df _ z£; (H - K H)^ 
^"~ 6 "" 6 ~ 6 

= ^ (I - K)3ft.-lb. 

The bending moment at any section P between B and C will be — 

B = |-^ Re (% - H + ^)| = |-g -g-j^ (a; - H + K H)| 

w x^ w}^^ X wYi^ w H^) , „ 
~6 6"K + 6'K 6^ J ""^• 

Differentiating B with respect to x — 

dB _w x^ w H^ 
irx~~2 6 K ' 

and for maximum bending moment, -j — = o, whence — 

w x^ _wR^ 2 _ H2 , _ H 

~Y~ - 6 K ''''■''« - 3'K' ""' ~ VsTK" 

Inserting this value of x in the expression for B — 

"''' ~ i8 V3T3 ~ 6\7jK^ + 6K ~ 6 
w H^ / 



I 



H3 / I i__ . I _ I^ 

6 V3 V3 K3 Val^ K V' 



and equating this with the expression for the bending moment at 
C (bearing in mind that the two moments are of opposite sense) — 

wW/ 1 I I \ _ _ '^ ^^ /t _ K^3 

6 \3 VrK3 V3 K3 "^ K V ~ 6 ^' "^^ ' 

which, on simplification, becomes — 

1-3 + 3 Vr^ = 3 VJK"^ {I - (I - K)3|, 

whence 3 \/3lC3 {i — (i — K)^} — 3 V3K + 2 = 0, 

or VK3 {i - (i _ K)3| - \/K + 0-385 = 0. 



WALLS OF RECTANGULAR TANKS 



105 



AXIS OF 
ANGLE 



This equation, in the form given, may be readily solved by means 
of a graph on squared paper, giving K = 0"524, whence — 

d = 0*524 H. 

With the rail fixed at this level, the maximum 
bending moment between B and C will be equal 
in magnitude to that at C ; hence, the latter (being 
more easily calculated) may be used for the purposes 
of designing. I h 

The rail should be fixed so that its axis (i. e. the 
centre of gravity of its cross-section) is at the level 
d, the dimensions being measured as indicated in 
Fig. 48. Obviously, the plate is more favourably 
circumstanced with this than with any other .c^.±..±- 

disposition of the rail C. 

Returning to the case of a 6 ft. depth, with the 
more effective placing of the rail — 

B C = ^ = 6 X 0-524 = 3-14 ft., and A C = 2-86 ft. 

Hence B, = '^i^'- = 62:iA|i:3937 = ^41 ft.-lb. 



Fig. 48. 



/24I X 12 
\ 2240 



in. -tons. 



With the resistance moment = 15 t^ in. -tons, as before — 

0'o86i, and t = \/o'o86i = 0*29 in.. 



2 _ 24 1 X 12 
~ 2240 X 15 



which renders a -f^ in. plate ample, with a reasonable allowance for 
corrosion, beyond mere strength requirements. 

The position of the section at which maximum bending moment 
occurs between B and C is easily found by inserting the value of K 

in the expression for Xq resulting from -3— = o. Thus — 

^^ H ^ H = ^ = ^ 

^ V3^ Va X 0-524 Vi*572 1*256 
= 0-798 H, or (very nearly) 0-8 H. 
Since d = 0*524 H, by subtraction, A C ^ 0*476 H, and the 
bending moment for purposes of design will be — 

■r> _'^ (0*476 H)^ . 
J5- ^ , 



io6 



TANK CONSTRUCTION 



which, for water, becomes — 



T3 62-2 X 0-10785 H^ o TTt rx 1U 

B = ^ — '—^ — = i-ii8i H^ ft. -lb. 

6 



I'liSi X 12 



2240 



(H^) in. -tons. 



With the resistance moment = 15 /^ — • 



whence 

and 

whence 



,2 i-iiSi X 12 X H^ TT1 

/2 = = 0*000300 H^, 

2240 X 15 ^^ 

t = \/o'ooo399 H^ = o'02 (VH^) in., 

^3 2240 X 15 X /2 ^ ,0 
H^ = ^ -7, — ^ = 2504 /% 



I'liSi X 12 

H = V25O4I2 := 13-58 {Vt^. 

Inserting appropriate stock values for t, the following table, 
comparable with those given in pages 90 and 98, may be con- 
structed — 



t = 

Thickness 

of Plate 

in Inches. 


Calculations. 


H = 

Maximum 

Permissible 

Head ia Feet. 


i 

1 

f 

H 
i 


</^504_X^.5 ^v.44-5 

</'"^ " V'35.-x 
^.504_X_49 ^ V479-3 

^ 4 

' /2504 X 81 a / 
^2504 X12X _ ,^,„g-,^- 


5-39 
6-25 
7-06 

7-83 
8-56 

9-25 

9-93 

10-58 

II-20 


^2504^x9 ^ .^,^^^g.^ 



On comparison, it will be seen that this arrangement permits 



WALLS OF RECTANGULAR TANKS I07 

depths more than 50 per cent, in excess of those for the curb at the 
brim, and more than double those for the wall plates flanged in one 
piece with the floor plates. 

36. — Effects of Variations in Liquid Head. — With regard to the 
arrangement of Fig. 48, the question arises as to whether the wall 
sheeting may be more severely stressed with the tank partly, instead 
oi completely, filled. For a tank of given depth, and having the 
rail C fixed at the most economical level for the maximum head, 
it is obvious that the Outward pressure of the liquid must diminish 
as the liquid head is reduced. On the other hand, however, since 
the rail C remains at its fixed level, the reaction R^ will be reduced 
as the surface of the liquid falls. 

The net bending moment in the sheeting between B and C is 
the difference between the moments due to these two opposing 
influences, and since the inward and outward moments follow 
different laws, it is not clear, from a superficial view of the facts, 
that the maximum bending moment in the sheeting with the tank 
full will of necessity be more than that with the surface of the con- 
tained liquid standing at some lower level. 

Moreover, the bending action changes in character as the liquid 
head varies. With the tank full, there is a point of contraflexure 
in the wall sheeting, and as the surface of the liquid falls between 
A and C, the point of contraflexure rises towards C. The surface of 
the liquid and the point of contraflexure arrive at C simultaneously, 
but the contrary bending moment due to the pressure of the liquid 
upon the portion of the sheeting above C, acting as a cantilever — 
which moment has become less and less as the liquid surface fell 
from A towards C, — vanishes as the surface of the liquid reaches C. 
As soon as the liquid surface reaches C, and for all less heads, the 
case becomes practically the same as that indicated in Fig. 43. 

From this it follows that as the liquid surface varies between 
A and C (Fig. 47), the stress at the wetted skin of the wall sheeting 
at C varies between the maximum working stress in tension and 
zero, while the stress at the outer skin varies between maximum 
compression and zero. The same variation in the level of the 
liquid surface causes the stress at that section of the wall sheeting 
which marks the point of contraflexure with the tank brim-full to 
vary between zero and a considerable compression at the wetted 



io8 



TANK CONSTRUCTION 



skin, and between zero and a corresponding tension at tlie onter 
skin. 

For all possible heads, the stress in the sheeting between B and 
either C or the point of contraflexure is compressive at the wetted 
skin, and tensile at the outer skin. 

It is clear that, with the liquid surface varying between C and 

B, the bending does not change in character; and it is also clear 

that, of all such cases, that with the liquid surface at C gives the 

most severe conditions as regards bending in the wall sheeting. 

Thus, the stresses in the portion A C may fluctuate between zero 

and a maximum ; while slightly below C 
the stresses are liable to alternation through 
a fairly wide range. 

These fluctuations and alternations of 
stress cannot occur rapidly, and it is there- 
fore probably unnecessary to make any 
provision for them by reducing the maxi- 
mum permissible working stresses. It will, 
however, be well to dispose of the ques- 
tion as to whether the wall sheeting is 
most severely loaded when the liquid 
surface stands at the brim of the tank or 
at some lower level, before passing on to 
the consideration of other cases. 

Taking the rail C as fixed at the most 
economical level for the maximum head 
H, let the variable (and lesser) head be represented by h, as 
indicated in Fig. 49. 

The reaction Re (per foot run) will then be — 

w h^ 

• nr It /J -^ /TT H K" - — ^ 

6K 




Fig. 49. 



Rr = 



6KH 



; or, if h = q H, Re = . ^- (q)^. 



At C the bending moment will be — 
^ _w (h-K H)3 



w H: 



(? - K)^ 



This expression is applicable for values of q between (and including) 
unity and K only — i. e. for levels of the liquid surface between 
(and including) A and C. Clearly, for all permissible values of h 



B = 



WALLS OF RECTANGULAR TANKS IO9 

less than H, the bending moment at C will be less than the ccrre- 
sponding bending moment with the tank full to the brim. 

With the surface level between A and C, as in Fig. 49, the 
bending moment at any section P between B and C will be — 

= 6^ — ^ + -^-^n- 

Differentiating B with respect to x — 

dx 6 1"^ K J' 

and for maximum bending moment, 3-^ = o, whence, maximum 
bending moment occurs at the section where — 



3%2 



H2^3 



K ' 

or, denoting this particular value of x as Xq — 



^0 = Vtk~ ^ °*^^^^ ^ ^' 



3K 

In passing, it is worth noting that this section of maximum 
bending moment remains at practically the same level in any given 
tank throughout almost the whole range of possible variation in 
the level of the liquid surface. 

The distances x and Xq are, of course, measured downwards 
from the surface of the liquid, as indicated in Fig. 49, and, as this 
surface is to vary, it will be well to locate the sections at which the 
maximum bending moments occur with reference to some fixed 
point — say, A, the brim of the tank. 

Then, the distances of the sections below A will be given by — 

^1 = ^0 + (H — h) = :^o + H (I — q), 
and inserting the value of Xq — 

x^^n (07976 Vf + 1 — q), 

which may be written as : ;ti = H (a). 

Giving to q the values i, 0*9, 0'8, 0*2, o*i, and 0, the 



no 



TANK CONSTRUCTION 



corresponding values of a may be calculated. These are as shown 
in the accompanying table, and indicate that the point of maximum 
bending moment rises by 0*03 H as the surface of the liquid falls 



q- 


a. 


<!■ 


a. 


I'O 


07976 


0-4 


o-8oi8 


0-9 


07812 


0-3 


0-8311 


0-8 


07707 


0-2 


0-8714 


07 


07672 


o-i 


0-9252 


0-6 


07707 





i-o 


0-5 


07820 







from H to 07 H, after which, further falls of the liquid surface are 
accompanied by very slight lower in gs of the section at which maxi- 
mum bending moment occurs, until the liquid head has been reduced 
to 0*2 H, when the point of maximum bending moment falls almost 
as rapidly as does the liquid surface. 

In a tank 10 ft. in depth, therefore, lowering the liquid surface 
from the brim to 3 ft. below, the section of maximum bending 
moment would be raised 3*65 in. Further reductions of head, 
down to a depth of only 3 ft., would lower the section of maximum 
bending mom.ent by about 7 "66 in., bringing it only about 4 in. 
below the level at which it stood with the tank full to the brim. 
Obviously, the effects with heads less than 03 H are unimportant. 

Substituting 07976 K V q^ for x in the expression for the bending 
momxent, a general relation may be obtained, giving the maximum 
bending moment between B and C for any level of the liquid surface. 
Thus- — 



■D 



wU^ f , ^ /-^. „ 07976 q^'^ 

— ^ I 07076 V^*^)^ — ^^^ ^ - , 

6 t ^^^ ^ ^ 0-524 0-524 ' J 



+ 



^ - ^3l 



This expression could be differentiated with respect to q, and 
the value of q giving the greatest maximum bending moment thus 
determined. The expressions obtained would, however, be rather 
awkward to deal with, and this may be left as an exercise for those 
having sufficient enthusiasm and leisure. 

Another method, probably more convincing, will suit our purpose 
equally well. 

(w x^ \ 
y = — >- ) of moments due 



WALLS OF RECTANGULAR TANKS 



III 



to the liquid pressure, as indicated in Fig. 50. The single curve 
may be used for all values of h by taking the base-line as much 
above the horizontal through O as the liquid surface is to be helow 
the brim. Thus, the moment curve for h = 9 ft. is the portion of 
the curve above the horizontal through i ; and so on. 

The diagram of moment due to Re may be drawn by means of a 
straight line joining the extremity of the liquid pressure curve with 
a point on the vertical axis 0*524 H (which is equal to 5*24 ft. in the 
case chosen) above the horizontal representing the floor of the tank. 
This, also, may be drawn for all heads on the single diagram, as 
shown. 




Fig. 50. 

Bending moments are shown by the horizontal intercepts 
between the straight and curved moment diagrams, as indicated, 
for clearness, in Fig. 51, which relates to the case for h = 0*9 H. 

A tangent to the curved line, parallel with the appropriate 
straight diagram line, will show the maximum bending moment 
between B and C for an}^ particular value of h. 

Every one interested in the matter should draw this diagram 
for himself. It is impossible to extract all the information by 
studying a complete diagram drawn by another. 

Upon investigation it will be found that the maximum net 
bending moment between B and C is greatest when h is about 0*9 H, 
its magnitude then being approximately 07 per cent, more than 
with the tank full to the brim — the liquid being supposed to have 
a specific gravity equal to that of water. This is so small an excess 



112 



TANK CONSTRUCTION 



that the relations previously obtained may be allowed to stand for 
all ordinary cases, and the permissible depths corresponding to 
stock plate thicknesses, as tabulated on page io6, may be used. 

The sheeting does, of course, receive a certain degree of assistance 
from the restraint imposed at B b}^ the ordinary riveted connection 
to the curb angle, and also from the resistance of the rail C to 
torsion, though such assistance is too uncertain and variable to be 
taken into account in the calculations. Such assistance may easily 
outweigh the effects of the increased loading, but with a tank of 
very great depth — or with a very heavy liquid to be contained — 




•J.ooo i.oeo 3,000 1.000 



Fig. 51. 



it might be well to provide some slight relief for the sheeting, rather 
than to increase its thickness throughout. 

Generally, it will be found that sufficient relief may be obtained 
by lowering the rail C slightly — so that its axis lies at a height of 
about 0*5 H instead of 0*524 H — and providing it with a fairly wide 
vertical limb. 

Lowering the rail C will assist the sheeting between B and C, 
and throw a slightly more severe bending moment upon it at C — 
as may be seen from a consideration of Fig. 50. In the nature of 
things, however, a tank can seldom be brimful, and hence the more 
severe loading at C is not likely to materialise. Moreover, the width 
of the rail C (vertically) will have the effect of distributing the 
reaction R^ to some extent, and therefore the diagram of net bend- 



WALLS OF RECTANGULAR TANKS II3 

ing moment will not have a sharp cusp at the level of C (as we have 
supposed), but will be rounded off, reducing the maximum intensity 
of the stresses in the sheeting at that level. 

Though it should be unnecessary to do so, it may be well to 
emphasise the fact that the permissible depths tabulated for stock 
plate thicknesses in the preceding examples are for water (or other 
liquids of equal density), weighing 62*2 lb. per cub. ft., and at 
ordinary atmospheric pressures. For heavier liquids, and for 
cases in which additional pressure may be applied — either by the 
liquid standing in a rising pipe above the top of the tank, with the 
roof tight against leakage, or by any other means — the tabulated 
values do not apply. Though it is hoped they may be of use in a 
considerable range of practical cases, these tabulated permissible 
depths are given primarily for the purpose of showing the com- 
parative merits of the various methods of staying the wall sheeting 
of tanks. 

37. — Walls with Several Horizontal Rails. — In view of the advan- 
tageous results which, as we have shown, are to be obtained by 
placing the horizontal rail C at a suitable level, it would seem 
reasonable to suppose that further advantage might be gained from 
the use of two such rails at appropriate levels — or even, with very 
deep tanks, of several rails. 

To a certain extent this is true, but, as will be seen presently, 
the arrangement of the sheeting must be altered if any appreciable 
saving is to be effected. 

With two horizontal rails, one might be placed at the brim to 
form a curb, and the other at some intermediate level between the 
brim and floor, as indicated in Fig. 52 ; or both rails might be 
between the brim and floor, as in Fig. 53, leaving a portion of the 
sheeting to act as a cantilever above the upper rail. 

We will consider the former of these arrangements, afterwards 
disposing of the latter by means of inferences to be drawn from the 
results of our investigation. As in the preceding cases, we shall 
ignore any partial fixity which there may be at the base connection, 
the wall being regarded as hinged — i. e. fixed in position, but not 
restrained as to direction — at B. 

The magnitudes of the reactions at A, B, and C will depend, 
of course, upon the relative movements permitted by the supports 



114 



TANK CONSTRUCTION 



at those levels, as well as upon the position of the rail C. We will 
first investigate the question on the assumption that no appreciable 
movement is possible at either A, B, or C ; and afterwards we may 
consider the effects of such movements as might be expected in 
actual cases. 

First it is necessary to determine the deflections of the wall 
plate, acting as a beam freely supported at A and B, under 
the action of the liquid pressure only, and supposing the rail C 
removed. It is, perhaps, easiest for this purpose to imagine the 
beam-strip as separated into two cantilevers, the cut being made 




B 




Fig. 52. 



Fig. 53. 



at the section where maximum deflection occurs, each cantilever 
portion being treated as " fixed " at that section. The conditions 
of loading and support for the complete beam-strip are indicated 
at (a) in Fig. 54, and those for the two portions to be treated as 
cantilevers at (b) and (c) in the same illustration. 

Then, from (b) in Fig. 54, the symbols retaining the meanings 
assigned to them for the cases already treated, the bending moment 
at any section P, distant x from O, will be — 

B _ I"- H^ (H -X)- "' '"' - ^)"l 



WALLS OF RECTANGULAR TANKS 



115 



whence 



w f 



d y _ I 
d x~ Y.1 ^ 



'Bv d X = 



g^j I ^H, (H^ - H,2) - 1 (H^ - 3 H^^) - H,;t3 + ^ + (C = O)) 

w i \ 



24 
and integrating again- 



r_2 



y = 



z£; 



24 E I 



{2 a;=Hi (H^ - H,^) - '^ (H2 - 3 Hi^) - ;,4 H, + I + (C = O)) 
=i6o"Eli30 :*;^ Hi (H^ - Hi^) - 10 ;t» (H2 - 3 Hi^) - 15 ;,4 H^ 4. 3 ^5} 

T 




Fig. 54. 

When ^ = Hi, y will be a maximum, and its magnitude will 
then be — 



% 



(max) 



^5j£j {30 Hi=' (H^ - Hi^) - 10 Hi» (H2 - 3 H,2) _ 15 H,5 + 3H,5j 
= 3l55'Er3°Hi'H'-3oH,= -ioHi»H2 + 3oH/-i5Hi^ + 3Hi5} 



ii6 



TANK CONSTRUCTION 



Another value of S may be obtained by reasoning from (c) in 
Fig. 54, and on equating these two values, the ratio borne by H\ 
to H will be obtained, and the section at which maximum deflection 
occurs will thus be located. To obtain an expression for the bending 
moment at any section P, distant x from O in (c), Fig 54, however, 
it is necessary to know the leverage of the resultant liquid pressure 
to the right of P, and, in order that our treatment may be reasonably 
complete, it will be well to establish this leverage in passing. 

The problem is merely to determine the horizontal distance 
between the centre of gravity of the area shown in Fig 55 and the 
axis Z Z. Dividing the area, by means of the dotted line, into a 




Fig. 55. 

rectangle and a triangle, the moment of the area about the axis 
Z Z will be— 

= ^-^ — 5-^ -' = 6 (2 ^2 + K)- 

/}i _i_ ^ \ 
The area is : A = / ( -^ '"^ ), and hence the required leverage will 



^^— _ M _ /2 2 _ / (2 ^2 + K) 

^ - A - 6 ^^ ^2 + ^1^ ^ / (h, + A,) - 3 (K + K) • 
Substituting for h^ and h^ the intensities of pressure at B and P 
respectively, and for I the distance (H — H^ — x), the leverage of 
the resultant liquid pressure to the right of P will be — 

(H - Y{^-x){2wYL-\-w(Y{^ + x)} ^ ( H-H^-a;) (2H + H^ + ^) 
3 {«; H + w(Y{^ + x)\ 3 (H + Hi + a;) 

_ f 2 H^^ - H Hi - Hi^ - a; H - 2 a; Hi - % 2) 

3(H + Hi + a;) /• 



fl = 



{ 



WALLS OF RECTANGULAR TANKS II7 

The average liquid pressure between P and B will be — 



JH + Hi + %| 



w c 
2 ' 

and this average pressure acting over the distance between P and 
B gives the total liquid pressure to the right of P as — 

^ (H + Hi + %) (H - Hi - x). 

Hence, the bending moment at P will be — • 

Bp = '"^ (H - Hi - %) - ^ (H + Hi + ^) (H - Hi - x) 

/ 2 H^ - H Hi - Hi^ - a; H - 2 ;t; Hi - a;^ \ 

I 3(H + Hi+%) J' 

which, on simplification, gives — 

Integrating — 

l^ = 6f-l{H^H>^+|(«^)-*H^^-¥(3H/)-.'Hi-^V(C=0)} 

= efi {^ "i< "' - "1') + f ("' - 3 Hi=) - xm^ - 

Again integrating — 

>' = ef-if-?" (H^ - Hi^) + ? (H^ - 3 Hi^) - f (Hi) -,t+ (C = O)} 

w 
= ^55e^ {30 x^ Hi (H2 - Hi2) + 10 %3 (H2 - 3Hi2) - 15 x^ Hi - 3^;^} . 

When X = {E. — HJ, y will be a maximum, and its magnitude 
will then be — 

^ '7H5- 3oH3Hi2 + 2oH2Hi3 + isHHi*- 12 H/} 



360 EI 

Equating the two values of 8 — 

20 H2 Hi=^- 12 Hi5=7 H5-30 H3 Hi^ + 20 H^ Hi^+is H Hi*- 12 H/. 

.-. 7 H^ - 30 H3 Hi2 + 15 H Hi* - O. 
Writing r H instead oi Hi (i. e. letting Hi = r H) — 
7 H^ - 30 H^ r^ + 15 H^ y* = O. 
/. H^ (7 - 30 ^2 + 15 ^') = O. 



ii8 



TANK CONSTRUCTION 



The equation : 7 — 3or^+i5^ = may be solved, by plotting 
upon squared paper or otherwise, to give ; r = 0'52 ; so that 
Hi = 0-52 H. 

Inserting this value of H^ in the first expression for 8 above — 

To neutralise this deflection by means of a single concentrated load 
midway between A and B — 

Re H^ _ 0*0065442 w W 

48Tn ~ EI ' 







Fig. 56. 



whence Re = 0*31412 iv H^. This will reduce the reactions at^A 
and B, each by 0*15706 w H^, giving — 

wH2 



Net reaction at A = 



Net reaction at B = 



6 

7^H2 



— 0*15706 w H^ = 0*00961 IV H^; and 

— 0*15706 z^ H^ = 0*17627 w H^. 



The complete loading conditions for the continuous beam-strip 
are, then, as indicated at [a) in Fig. 56; the component and net 
bending moment diagrams as at {h) ; and the net bending moment 
diagram, reduced to a vertical axis, and the ordinates to an enlarged 
scale, for clearness and convenience of examination, as shown at 
(c) in the same illustration. 



WALLS OF RECTANGULAR TANKS JK) 

The figured ordinates of the diagram at (c) in Fig. 56 repre- 
sent the bending moments, in foot-pounds, for the case in which 
H = 10 ft., calculated from the expressions — • 



B(A 



and 



(W X^ ^ ] f W X^ r TT2 1 . 

to c) = ( 5 — Ra ^I = j-g — 0-00961 wW-xy, 



B(ctoB; = |-g Ra a; - Re (^a; - ^ 

fw x^ / HW 

= I ~j- — 0*00961 wYL^ X — 0-31412 wH^\x — —\\. 

Taking the weight of the contained liquid as w = 62-2 lb. per 
cubic foot, these expressions may be simplified to — • 
B,A to c, = {^ (10-37 ^^- 60} ; and, B,c to b) = {^ (10-37 ^'-2014) + 9770}, 
from which the figured ordinates may be calculated. 

Now, if the bending moment diagram shown in Fig. 56 be com- 
pared with that (see Fig. 47) for the single rail at C, it will be 
found that there is practically no difference between them — cer- 
tainly not sufficient to permit a reduction of y\- in. in the plate 
thickness for ordinary tank-depths. Moreover, in the arrange- 
ment of Fig. 52 there are two rails as against one in the case of 
Fig. 47, and this extra cost would not be recovered. 

The pressure upon the rail C — about 17-5 cwt. per foot-run with 
a tank 10 ft. in depth — is so much that, even with a very stiff (and 
therefore costly) rail, some outward movement of the plating at C 
would be inevitable. This would have the effect of reducing the 
bending moment at C, and increasing it between C and B, so that 
the plating, with this arrangement, might be subjected to more 
severe loading than that with the arrangement discussed in 
pp. 100-113. 

Further, in view of the circumstances of loading and horizontal 
support, it would be practically impossible to estimate the extent 
of movement likely to occur at C with sufficient probability of 
truth to render any design for the sheeting, based upon such esti- 
mated movement, reasonably dependable. 

No useful purpose would be served by raising the rail C — indeed, 
quite the reverse; nor would matters be improved by lowering 
the rail C, for the pressure upon it would be considerably increased, 



120 TANK CONSTRUCTION 

and the degree of movement permitted in the sheeting more 
problematical than before. 

With very deep tanks there might be a certain amount of advan- 
tage to be gained from the arrangement of Fig. 53, though this 
advantage would be lost as soon as the liquid surface fell to the level 
of the upper rail. 

It would seem, therefore, that the only advantageous way to 
utilise two or more horizontal rail supports for the side-walls would 
be to let the sheeting lie in horizontal strakes, bearing upon a rail top 
and bottom, and not attempting to secure either continuity or 
uniformity of support. 

38. — Walls with Vertical Siiffeners. — Vertical stays may be 
employed, instead of horizontal rails, to support the side walls 
against overturning. 

This method (which is widely used) we shall now consider, 
though the author is of opinion that, as a rule, for rectangular tanks 
of ordinary dimensions and proportions, the properly placed 
horizontal rail, as indicated in Fig. 48 (p. 105), provides the 
most satisfactory and economical form of wall support. 

An arrangement in common use is shown in Fig. 57, the vertical 
stays being generally of an angle bar, riveted to the bottom and top 
curbs. Clearly, if the vertical stays are to act as beams, the top 
curb must be capable of providing the upper reactions, and should 
either possess sufficient strength and stiffness of their own for this 
purpose, or be themselves adequately stayed in some convenient 
manner. 

At the outset we are met with the difficulty of determining as 
to how the wall plating acts in transmitting the horizontal pressures 
to the stays. Obviously, from Fig. 57, it it were not supported by 
the floor and top curbs, the plating would act simply as a beam 
between the stays, and the design would then be a simple matter. 
At the floor, however, the wall plating must be securely fastened to 
the curb angle, in order to prevent leakage, and the question is 
thus raised as to the effect, as regards nature and extent, which 
this has upon the action of the plating. No profound argument is 
needed to show that the ultimate effect of closely riveting the 
plating to the bottom curb must be to increase its strength and stiff- 
ness in its lower portions, and the question remaining is as to the 



WALLS OF RECTANGULAR TANKS 



121 



manner in which the additional strength is imparted to the plating, 
and the extent to which it may properly be relied upon in designing 
tanks for commercial purposes. Obviously, to design the plating 
on the basis of a beam strip spanning between the vertical stays, 
and subjected to the full intensity of pressure exerted by the con- 
tained Hquid at the tank floor, would be to waste material, but it is 
not easy to see what allowance should be made for the additional 
strength imparted to the plating. 

So far as the author is aware, no satisfactory solution of this 




FRONT ELEVATION. 



SECTION 



Fig. 57. 

question, based upon rigid analysis, has yet been obtained ; and it 
would seem unlikely that any such solution, applicable to the 
practical design of tank walls, will be found. 

Various formulae have been deduced for the stresses set up in 
flat plates supported or fixed at all their edges, but it is at least 
doubtful whether such relations can be employed, with any degree 
of reliability, in designing the wall plating for rectangular tanks. 
Most of these formulae are based upon assumptions regarding 
the distribution of loading to give equal deflections (or, more 
strictly, the same deflection) in two beam strips of the plate inter- 
secting at right angles ; but while there can be no doubt that some 
such distribution of loading is automatically effected, the deflection 



122 TANK CONSTRUCTION 

produced at any particular part of the plate must depend upon 
several factors which, from their nature, cannot be accurately 
foreseen, nor satisfactorily provided for, on a basis of assumption, 
in circumstances such as those occurring in tank work. 

For instance, the actual and relative degrees of stiffness in the 
supports cannot fail to influence the local deflections in the plate, 
and since these degrees of stiffness are inevitably different at the 
different edges of the plate-panels — besides being variable from 
point to point along some edges while others are sensibly rigid 
throughout — it is practically impossible to deduce an expression 
which shall take proper account of the variations probable or possible 
in the framing of an ordinary tank. It is clear from Fig. 57 that 
the plate will be, to all intents and purposes, rigidly supported along 
the bottom curb, but the vertical stays and top curb will be subject 
to elastic deflection under loading. ^Moreover, even if the upper 
ends of the stays be fixed in position, the elastic lines of the stays 
will be unlike that of the top curb, for the loading upon the latter 
will be uniform — or, at least, symmetrical — while that acting upon 
the stays will increase from a minimum near their upper ends to a 
maximum near their lower ends. 

Further, the plating of a tank wall of the type under discussion 
is always continuous over some of its supports (viz., those vertical 
stays at which no seam in the plating occurs) ; subject to more or 
less partial restraint as to direction at others (the bottom curb) ; and 
perhaps almost freely supported at others (the top curb). 

Thus it will be seen that irregularities and inequalities are possible 
in combinations covering a range so wide as to render it unlikely 
that any single expression could take them into account, even 
approximately, and remain usable in ordinary practical designing. 

As an alternative, the author would suggest the following argu- 
ment as being at least equally reasonable, while yielding a more 
simple basis for practical design. 

Consider the panel of plating indicated in Fig. 58, freely sup- 
ported along the edges A D, B C, and C D, and unsupported along 
A B, subjected to transverse loading such as would be applied by 
liquid pressure — i. e. varying uniformly in intensity from zero at 
A B to a maximum at C D. The supports at A D and B C correspond 
to the vertical stays of a tank wall, and that at C D to the bottom 



WALLS OF RECTANGULAR TANKS 



123 



curb. We are ignoring the lateral supporting effect of the top curb 
(along A B) because it is usually formed of a light angle bar only, 
which could not be relied upon to influence the distribution of the 
loading, especially as the height (A D) of the panel is generally about 
double of its width (AB), and the intensities of pressure in the 
neighbourhood of A B are small as compared with those nearer C D. 

Now, even though the supports 
A D and B C may yield through 
elastic deflection, the movements 
in the portions near their lower 
ends, from this cause, will be ex- 
ceedingly minute, while the plate 
may be taken as fixed in position 
along the edge C D. 

Let us consider the effects of 
an element of pressure in some 
position such as E in Fig. 58. It 
will tend to cause deflections in 
many beam strips, two of which 
are indicated as F G and H K ; but 
the resistance of F G to such deflec- 
tion will be far more than that of 
H K, and hence a much greater 
proportion of the load at E will be 
taken by the strip along F G — 
indeed, strips parallel with F G up 
to about I ft. in length will be Fig -g. 

sensibly rigid. Similar conditions 

will, of course, obtain in the neighbourhood of the corner D, the 
plate being very stiff along such strips as F^ G^. 

Proceeding inwards from C and D it is obvious that a stage will 
somewhere be reached at which the stiffness of the plate along a 
strip parallel to F G will be not more than that parallel with H K, 
and ultimately, at some horizontal strip such as S S, the plate will 
receive little or no assistance from the support along C D. 

From observations made, the author is inclined to the view that 
this disappearance of the additional stiffness occurs, in ordinary 
cases, at a height (above the bottom curb) of about one-half to 



,. . . — 

i 


; 

^THIS EDGE NOT 
• SUPPORTED 


B 




PLATE SUPPORTED 


*■ 


"r 


ALONG TMEISE TNNO 


— -*. 




ED6ES AND BOTTOM. 








s 




F/ 

/ 


LP-.-- 


.>.vQ!--.G^..---- 


c 



124 TANK CONSTRUCTION 

two-thirds of the distance between the vertical stays — that is to 
say, the panel may be designed on the basis of a narrow beam strip 
S S, subjected to the pressure intensity corresponding to a liquid 
depth B S, taking S C = J C D, and ignoring the greater intensities 
of pressure below S S. The author hopes, however, to make further 
observations and tests, and may have more to say on this point 
later. 

We have considered the panel as freely supported along A D, 
B C, and C D, with the object of simplifying the discussion. The 
argument would, however, apply equally to the case of a plate 
continuous over the supports A D and B C, while the stiffness 
of the plate along strips as F G and F^ G^ will ^be so great that, 
in all probability, any partial fixity as to direction which the plate 
may receive through being riveted closely to the bottom curb 
(along C D) will not appreciably affect the inference for practical 
purposes. 

Hence, in the design for an actual case, if the plating were not 
restrained as to direction at the supports A D and B C, the strip S S 
should be regarded as freely supported at its ends ; while the same 
strip might be treated as " fixed " or " built-in " at its ends if the 
plating were continuous over the vertical stays, with all panels of 
equal width. 

For the purpose of comparing the arrangement indicated in 
Fig. 57 with those dealt with in the preceding pages, let us consider 
the relationship existing between the liquid head and plate thickness 
for a given width of panel. 

Taking the liquid head above S S (Fig. 58) in inches as H, and 
considering a beam-strip of the plating i in. in width at the level 
SS, the total pressure acting upon the strip will be (w H L) lb., w 
being the weight of the liquid in pounds per cubic inch, and L the 
length of span S S in inches. The maximum bending moment in 
the strip — if it be continuous over the vertical stays — will be — 

B = ) m.-lb. — ) m.-tons, 

V 12 / \ 12 X 2240 / 

The strength modulus of the section will be ( > V where i is the 
thickness of the plate in inches ; and taking a maximum permissible 



WALLS OF RECTANGULAR TANKS 12$ 

stress /= 7*5 tons per sq. in., the resistance moment oi the strip 
will be — • 



R = (^^V-) = (i'25 t^) in.-tons. 



Equating the resistance and bending moments — 
= 1-25 t^, 

12 X 2240 

whence — ■ 

12 X 2240 X i'25 i^ 33,600 t^ 



H = 



w L^ w IJ' ' 



/62'2\ 

If the contained liquid be water, taking ?x; as ( — ^ j lb. per cub. 

in. — 

33.600^^ X 1728 _ / t\^ 

^- 6^^U? - 933,454 I^lJ- 

As was to be expected, the permissible liquid head above S S 
varies directly with the square of the plate thickness, and inversely 
as the square of the panel width. Hence, plate thicknesses can only 
be tabulated with the corresponding liquid heads for a constant 
panel width. Such tables may easily be constructed, to cover the 
range of panel widths likely to be used, but there seems no need to 
include them here. A few typical instances will serve our purpose 
for comparison. 

Taking the case of a f in. plate with a span of 36 in., 

\1.) V 8 X 36 y 9216' 
whence — 

H = 933:^ = loi in. . 

9216 

Adding half the panel width (i. ^. — = i8 in.), the total permissible 

height above the tank floor would be loi + i8 = 119 — or, say, 
10 ft. A plate thickness of | in. with the arrangement of Fig. 48 
gave a permissible head of 706 ft., and hence, an additional 3 ft. of 
depth is obtained in return for the cost of the vertical stays at 3 ft. 
centres. 



126 TANK CONSTRUCTION 

With I in. plate over a 48 in. panel, 

tV/iV I 



4 X 36/ 20,736' 
whence — 

H = 933454 _ i„, 
20,736 ^^ 

Adding half the panel with (i. e. =24 in.), the total permissible 

head above the tank floor would be 45 + 24 = 69 in. = 575 ft. A 
plate thickness of J in. with the arrangement of Fig. 48 gave a 
permissible head of 5*39 ft., and hence, no appreciable advantage 
as regards depth is obtained by using vertical stays at 4 ft. centres 
instead of a horizontal rail; while the cost would almost certainly 
be greater with the arrangement of Fig. 57 than with that of Fig. 48. 
Perhaps a more definite comparison may be obtained as follows — 
With the arrangement of Fig. 48, a f in. plate thickness gave a 
permissible head of 7*06 ft., and for this head with the arrangement 
now under discussion we should have — 

H = (7-06 X 12) -(-- 

Taking ( — j as 2272 in. (obtained from a first approximation) — 
H = 8472 — 2272 = 62 in. 

.*. 933,454 (^) = 62 in. 

Inserting | in. for t, and transposing- — 

L2 _ 93 3454 X 9 _ 8401,086 _ 

62 X 64 3968 '' 

.*. L = \/2ii7 = 46 in. 

Now, the cost of the top curb with the arrangement of Fig. 57 
would probably not be appreciably less than that of the horizontal 
rail for the arrangement of Fig. 48, and taking other factors as 
similar in both cases, the cost of the vertical stays at about 3 ft. 
10 in. centres — or, at least, a large proportion of that cost — would 
appear to be outstanding to the detriment of the arrangement 
indicated in Fig. 57. 



WALLS OF RECTANGULAR TANKS I27 

Another instance will, perhaps, suffice. 

With the arrangement of Fig. 48, a wall of J in. plate gave a 
permissible head of 5*39 ft., and for this head with the arrangement 
of Fig. 57 we should have — 

H = (5-39 X 12) - ^ 



Taking - as I7"68 (obtained from a first approximation) — 
H = 64-68 — 17*68 = 47 in. 

/. 933,454 ( £ ) = 47 in. 

Inserting J in. for ^, and transposing — 

L2 ^ 933,454 ^ 933,454 ^ ^.^ 
16 X 47 752 

.'. L = V1241 = 35'2 in. 

Hence, for walls of J in. plate, the cost of the vertical stays at 
about 3 ft. centres would appear to be outstanding to the dis- 
advantage of the arrangement indicated in Fig. 57, as compared 
with that shown in Fig. 48. 

39. — Arrangement of Curbs, Rails, and Stiffeners. — We may con- 
clude our discussion of this class of walls for rectangular tanks with 
a few remarks upon the arrangement and fitting of curbs, rails, 
and staj^s, and the means for providing them with the necessary 
strength and stiffness to take up the pressures which may be applied 
to them. Also, as to the salient facts regarding the influence of the 
vertical stays upon the sheeting with respect to the continuity of 
the latter; and the assumptions regarding continuity which may 
properly be applied under given conditions. 

Bottom angle-curbs are invariably placed inside the tank, and 
for obvious reasons this is the best arrangement. It is the usual 
practice to place top curbs on the outside of tank walls, and this 
again, from all practical points of view, is as it should be. 

Vertical stays, however, should be placed on the outside of the 
tank walls, instead of inside as is practically always done. With 
the stay (or stiffener) inside the tank, as indicated at (a) in Fig. 59, 
the outward pressure of the contained liquid upon the wall sheeting 
must be transmitted to the stay by means of rivets or bolts, each one 



128 



TANK CONSTRUCTION 



of which must be made tight against leakage. This involves a 
large amount of drilling, riveting, and caulking — three items which 
should be minimised — as well as time and labour. With the stay 
placed outside the tank, as at (b) in Fig. 59, the wall sheeting 
is pressed against its support by the contained liquid, and only a 
few rivets are required to hold them in their proper relative positions. 




ELEVATION 



ELEVATION. 



k 



il^ 



2 ' y ■ r •^ ^ 




^ ^^1 vj^ i V i >k >^ 






SECTIONAL PLAN. 



SECTIONAL PLAN. 



Fig. 59. 



The sheeting itself is affected by this question, as well as the cost 
of the stiffeners. With sheeting continuous over the stiffeners, 

the maximum bending moment ( ) in the sheeting occurs at 



12 



the stiffeners, and the full section of the beam strip at these sections 
has been assumed in the foregoing examples. Now, it is obvious 
that a considerable number of rivet-holes through the plate must 
appreciably reduce its strength, and that at the most severely 



WALLS OF RECTANGULAR TANKS I29 

stressed sections. It is true that the rivets take up some of the 
bending action through their heads, but this is scarcely a factor to 
be rehed upon, and the advantages of the arrangement shown at 
(b) — as compared with that shown at {a) — in Fig. 59, from this point 
of view, will be obvious. Tacking rivets, of small diameter, at, 
say, 12 in. pitch, should be quite sufficient to keep the sheeting 
always in contact with the stiffener for the purpose of preventing 
atmospheric moisture from finding its way between them and causing 
corrosion. 

If it be objected that, since there are many tanks working 
satisfactorily with inside stiffeners, and with panel widths and liquid 
heads quite as large as those estimated in the foregoing examples 
for the plate thicknesses there stated, the weakening of the plate 
by the rivet-holes at the stiffeners must be negligible, there would 
still be a good reply. The weakening of the plate is undeniable, 
and the extent of the weakening cannot be otherwise than appre- 
ciable ; hence, either (or both) of two things must be happening in 
such tanks — (i) a greater intensity of stress than 7 "5 tons per sq. in. 
in the sheeting is being withstood, or (2) the sheeting is not acting 
as a continuous beam in the manner assumed, but is transmitting 
the pressures in some other way. 

Now, it has been stated above that there is a wide scope for 
careful and thorough investigation, by some competent and dis- 
interested observer, into the question of tank sheeting, with the 
object of ascertaining, as precisely as may be, both the manner in 
which the pressures are actually transmitted by the sheeting, and 
the working stresses which may properly be permitted — or, at least, 
allowed for in calculations — in the material. As has already been 
suggested, it is quite possible that the sheeting does not act as a 
series of beam-strips at all in some types of tanks — particularly 
that illustrated in Fig. 57 — and if this were so, it is obvious that a 
design based upon beam action at a stress of 7*5 tons per sq. in. 
could not (except by accident) be justified by fact. 

In the absence of established knowledge, however, we can only 

proceed by means of logical argument based upon what seem to be 

the most reasonable probabilities ; and if the sheeting does act as a 

series of beam-strips, then, as we have shown, a working stress of 

7*5 tons per sq. in. is the maximum which should be permitted 
K 



130 TANK CONSTRUCTION 

(in calculations) for British Standard mild steel as used for con- 
structional purposes. 

Moreover, the above objection would draw the reply that if a 
certain plate thickness is found sufhcient in fact for a given panel 
width and liquid head with the vertical stiffeners arranged inside, 
as at (a) in Fig. 59, then it is practically certain that sheeting of 
some less thickness would be sufficient with the arrangement shown 
at (b). 

Let it not be thought, from the foregoing admission, that the 
whole basis of design employed in these pages may be hopelessly 
false. It is only the method of staying indicated in Fig. 57 which 
is open to serious suspicion, and that for the reasons stated in the 
discussion of that particular method. 

Horizontal supporting rails, such as that indicated in Fig. 48. 
should be placed on the outside of the tank walls, for the same 
reasons as those which apply to similar placing of vertical stiffeners. 



CHAPTER V 

FRAMING FOR RECTANGULAR TANKS 

40. Horizontal Ties. — The best methods for providing horizontal 
rails or curbs with sufficient strength and stiffness for the proper 
transmission of the pressures which may be applied to them will 
depend upon, and should be governed by, the conditions and 
circumstances of individual cases. 

In a tank of comparatively small width, horizontal ties may be 
used, connecting the curb or rail at one side with that at the other 
side, as indicated in Fig. 60, thus utilising the outward pressures 
at one side to counteract those at the other side. 

If fiat steel bars are used for these horizontal ties, they should 
be placed as at {a) in Fig. 60 — i. e. with the greater cross-sectional 
dimension vertically — so that they may not sag unduly. As has 
been explained before, however, angle bars are preferable to flat 
bars for all such purposes, being at once more convenient to handle 
and fix, and also more effective in action. An angle bar tie should 
be placed as at [h) in Fig. 60 — i. e. with its horizontal outstanding 
limb uppermost — to give as much stiffness as possible in the com- 
pression flange. 

A convenient and effective method for attaching a horizontal 
transverse tie of angle bar to an external top curb is shown at {h) 
in Fig. 60, and at (c) in the same illustration is indicated an arrange- 
ment suitable for connecting the angle bar tie with an internal 
horizontal rail. Where the horizontal rail is placed on the outside 
of the tank wall, the tie may be connected with it by means of an 
internal cleat, riveted to the rail through the sheeting, as shown at 
[d) in Fig. 60. 

If it be desired to use an angle bar tie of a section so slight in 
relation to its span that considerable sagging would be likely, stiff- 
ness may be obtained by means of light trussing, as indicated in 

131 



132 



TANK CONSTRUCTION 



Fig. 6i. As a rule, however, it is found that such work increases 
the cost of the tank much more than would the use of an angle bar 





PLAN 



PLAN 




Fig. 6o. 



possessing sufficient strength and stiffness to properly cover the span, 
because of the labour involved in the trussing. Cases may — and 
do — arise in which the higher cost is less objectionable than the 
inconvenience which would result from an alternative method, and 



FRAMING FOR RECTANGULAR TANKS 



133 



for that reason the method should not be either condemned or 
ignored. 

Horizontal transverse ties are sometimes carried across very 
wide tanks, sagging of the ties being prevented by means of posts 
or standards, erected on the floor of the tank, as indicated in 



ANGLE. BAR TIE. 




flat bar ties 
Fig. 61. 



Fig. 62. There is no serious objection to urge against the use of 
such ties thus supported, though it is probable that, in general, 
better results might be obtained from somewhat less crude methods. 
The posts or standards should, of course, be placed directly over 
a bearer in every case, and should be so cleated as to possess adequate 
stability for their purpose. 



ANgLf BAK TIE 




m ^ 




Plan 



Fig 62. 



Fig. 63. 



It should be observed that the post or standard method of 
supporting very long ties has this advantage over the truss method 
of Fig. 6i^that with the former the tie has simply to carry itself 
from standard to standard; whereas, with the latter, in addition 
to its having to carry itself from strut to support (probably about the 
same distance as from standard to standard with the method of 
Fig. 62), it must act as the compression boom of the truss, and will 
thus be called upon to bear a more or less considerable axial thrust, 



134 



TANK CONSTRUCTION 



which may call for bracing or support laterally in the horizontal 
plane as well. 

With a very narrow tank the curbs or rails on the end walls 
may not need lateral support. Should such support be necessary, 
however, it may be provided satisfactorily by means of light framing 
to form a truss, using the nearest of the side-wall ties to form the 
compression boom, as indicated in Fig. 63. 

The side-wall tie which forms the compression boom of this 
truss may be supported against flexure in the vertical plane by 
means of either a light trussing, similar to that indicated in Fig. 
61 ; posts or standards, as in Fig. 62 ; or raking props from the 

bottom curb, as shown at {a) in 
Fig. 64. Sometimes the weight 
of such truss framing is carried by 
means of slings from above, as 
* ^ I °F ^r ^ indicated at (b) in Fig. 64. Where 

7/ ,^ \^ the rail to be stayed is a top 

curb, the sling support is, of 
course, impracticable ; but even 
where the rail is so placed lower 
down the wall as to render sus- 
pension from above the easier 
way of supporting the inner boom, 
it is still preferable to use the 
prop arrangement shown at (a) in Fig. 64. The bracket action set 
up with the latter will cause a restraining influence upon the wall ; 
whereas the bracket action set up by the sling support from above 
causes an additional bending action on the wall, of the same sense 
as that due to the pressure of the contained liquid. 

Horizontal transverse ties should be reasonably straight, care- 
fully fitted, and so adjusted as to be properly up to their work. 
Slackness (due to careless fitting or adjustment) or kinks in such 
ties will in all probability be the means of permitting movement, 
with consequent uncertainty as to the distribution of loading and 
intensity of stress in the various pieces, as well as other effects which 
are highly undesirable in riveted plate work. 

For the same reasons, the ties and their connections should be 
of such dimensions and proportions as will prevent any high intensity 




Fig. 64. 



FRAMING FOR RECTANGULAR TANKS 



135 



of stress, either generally or locally, from the loading likely to be 
appUed to them. Angle cleats should be sufficiently stiff to hold 
the ties without undue deformation, and not less than two rivets 
should be permitted for securing any piece, either to another member 
or to a cleat, gusset-plate, or other connecting piece. 

41. Trussed Framing. — Where a tank is too wide to permit the 
efficient use of transverse horizontal ties from wall to wall, the 
horizontal curbs or rails may be provided with sufficient strength 
and stiffness by means of truss-framing, as indicated in Fig. 65. 
The rail or curb will form the tension boom of this truss, and must 
also be designed to properly withstand the local bending caused by 
its action as a beam providing lateral support for the sheeting 
between the panel points. The inner 

boom of the truss will, of course, be 
subjected to compression, and will 
almost certainly need support to 
prevent it from falling vertically. 
Such support may be provided by 
means of light trussing, as in Fig. 
61 ; posts or standards, as in Fig. 62 ; 
or raking props, as at [a) in Fig. 64. 

Various modifications of this 
method, and combinations of truss- 
framing with horizontal transverse ties, will doubtless suggest 
themselves. A fairly obvious instance, for a tank of unusually 
great width and length, is indicated in Fig. 66. For such very 
large tanks, however, it is doubtful whether such methods are really 
economical. As will be shown presently, a better treatment for 
such cases may sometimes be obtained by using a framed tank, in 
which the wall framing is provided with sufficient stability to resist 
overturning, and thus needs no additional staying. 

42. Raking Slays. — Raking stays, indicated in Fig. 67, should 
not be employed if any other method of supporting the walls is 
practicable. The vertical component of the axial load applied to 
the raking stay is applied as a downward load upon the curb or 
rail, and practically the whole of this downward load must obviously 
be taken by the wall sheeting as a compression — a highly undesirable 
state of affairs. At the foot of the stay, a similar load is applied 




PLAN 



Fig. 65. 



136 



TANK CONSTRUCTION 



horizontally to the floor sheeting, unless the stay be secured to a 
substantial bearer lying in the vertical plane which contains the 
stay — and even then it is probable that transverse loading will be 
applied to some of the steel bearers, or other construction supporting 
the tank, which it is much better to avoid if possible. In framed 
tanks, raking stays are less objectionable, as the induced thrusts 
may be confined to regular constructional members, and thus be 
properly provided for. This point will be fully dealt with in due 



course. 




RAKINS STA.r 



PL^N 

Fig. 66. 




Fig. 67. 



43. Action of Curbs and Rails. — Let us consider the conditions 
of loading under which a top curb or horizontal supporting rail 
for a tank wall must act. 

It is often stated that a rectangular tank tends to assume a 
cylindrical form under the pressure of the contained liquid; and 
this, if interpreted broadly, is true. The tendency would be reahsed 
if the material of the containing walls were perfectly flexible — i. e. 
incapable of resisting bending actions while possessing adequate 
strength in tension. In ordinary tank work, however, this is not 
the case, and a somewhat closer examination of the facts is therefore 
necessary. 



FRAMING FOR RECTANGULAR TANKS 



137 



Consider the simple case of the top curb or horizontal supporting 
rail, without stays or bracing, for a tank square on plan, as indicated 
in Fig. 68. The tendency will be for the curb or rail to become 
distorted, and to take up some form such as that indicated by the 
dotted lines. 

Obviously, with so much distortion as is shown in the sketch, 
and assuming the tank floor to retain its shape, there would be 
wrinkling in the wall sheeting to such a degree as could not be 
tolerated in an actual tank. It is necessary, therefore, that the 
curbs or rails be provided with adequate stiffness to prevent undue 
bulging of the walls. 

The outward pressures upon each pair of opposite walls must 




iniiiinn 



Y 



YyVYTYYTTYT 



Fig. 68. 



Fig. 69. 



be taken up as a tension in the rails supporting the adjacent walls, 
this condition being as illustrated in Fig. 69. In addition, each 
rail must act as a beam in supporting its own wall against the 
outward pressures. 

The dotted lines of Fig. 68 imply that there is no stiffness at 
the corners of the tank, that each wall has its own separate rail, 
and that the rails are connected at their adjacent ends by means 
of hinged joints. 

If the rail or curb were of uniform (and, of course, adequate) 
.strength and stiffness throughout — at all four corners of the tank, 
as well as along the walls — the tendency to opening at the corners 
would be resisted. The rail would then take up some form such 
as that indicated in Fig. 70, and the distortion would be less than 
with the rails hinged at the corners. 



138 



TANK CONSTRUCTION 



Clearly, the benefit of this continuity would be reduced if the 
tank were rectangular in plan instead of square, for the total pressures 
upon the shorter sides would not be sufficient to balance those 
acting upon the longer sides. 

For the purposes of investigation, we may imagine the con- 
tinuous rail to be cut at one of the corners, the rail straightened, 
appropriate supporting forces and restraining couples applied at 
the cut ends and corner points to reproduce the conditions before 
cutting, and loading applied equivalent in all respects to that set 
up by liquid pressure in the tank. 

The conditions for a square tank would then be as indicated in 
Fig. 71, and those for a rectangular tank as in Fig. 72, the difference 




Fig. 70. 

between the two sets of conditions, as regards fi^xural tendencies, 
being apparent. 

In practice, it would be a comparatively simple matter to 
reproduce these conditions of continuity in the top curb. The 
lengths of the walls would probably always be so short as to obviate 
joints in the rails except at the corners of the tank, and these might 
be gusseted, as shown in Fig. 73. The sketch indicates a curb of 
angle. bar, and this is by far the most usual form; it is, however, 
not necessary to limit the section to an angle bar, any convenient 
section (either rolled or built-up), suitable for taking up the loading, 
being applicable. 

For the curb on each wall of a tank square on plan, therefore, 
the conditions of loading would be as indicated in Fig. 74, and the 
investigation for design presents little difficulty. 



FRAMING FOR RECTANGULAR TANKS 1 39 

To avoid unnecessary complication in the work, let us suppose 









J 

r 

> 

> 

> 

— ► 
> 

> 

> 

» 

> 

> 

> 

> 

.- — > 

> 

> 

> 


< 

< 

"< 

-^ 



01 



KSJ- 



that the pressure apphed to the curb by the sheeting has been 
determined, and let this pressure be taken as w lb. per foot run of 
curb. Then, if the length (and breadth) of the tank be / feet, the 



140 



TANK CONSTRUCTION 



total transverse load upon the curb will he w I lb. At each end 
there will be a reaction equal to ( — ), supplied by the tensile 
resistance of the curb on the adjacent wall. In addition, there will 
be a couple at each end, of magnitude equal to Iw 1 1 j ■ , and also 

a longitudinal tension equal to (^^ j, applied by the curb on the 
adjacent wall. 



e e ® \ 



Fig. 73. 

The maximum tensile stress in the curb section will thus be — 

/ _ ^' ^^ I !^ _ivl /A I -\- 6M 
^ ~ i¥M "^ 2A ~ T \"6 A M 

where A is the area, and M the modulus, of the effective curb section. 
Taking/ as 16,800 lb. (= 7*5 tons) per sq. in. for mild steel, and 
transposing — 

AM \ wl ' 



A / + 6 M 



201,600 



With any particular type of section, over a likely range, there 
is always a roughly approximate relation between A and M — e. g. 
with equal angles in the neighbourhood of 3 in. x 3 in. x ^ in., A= 
2*5 M ; for larger angles up to 4 in. X 4 in. x I in., A = 2 M ; and 
so on, — and by making use of this fact, guiding values for A and M 
may be readily obtained. 

Differences of opinion sometimes arise as to whether any — and, 



FRAMING FOR RECTANGULAR TANKS 



141 



if so, how much — of the wall sheeting may be regarded as forming 
part of the effective curb section in taking up the loading. 

This question must, clearly, depend to a large extent upon the 
connections and riveting of the tank. It would be illogical, for 
instance, to calculate upon a certain sectional area of the sheeting, 
as forming part of the effective curb section, if the rivets securing 
the curb proper to the wall sheeting were not sufficient to develop 
the strength of more than a small fraction of that area. Nor would 
it be economical to ignore the wall sheeting entirely if the curb 
riveting were capable of developing the strength of a considerable 
area of it. 

In ordinary circumstances, the wall sheeting in the neighbourhood 
of the top curb is very lightly stressed from the direct liquid pressure 



w 



I 




TYX YVYNrrYYVT 




Fig. 74. 



upon it, and hence it would seem a wise course to utilise as much 
of it as possible in building up the effective section of the curb. 
From the practical point of view, however, there may be other 
considerations which would turn an apparent economy into an 
actual extravagance. 

For example, it might easily be that the cost of providing 
sufficient additional rivets to develop the strength of a desired area 
of the wall sheeting would far exceed the cost of the bare material 
which, by using a larger bar of the same type for the curb proper, 
would give the required strength. Moreover, the top curb is one 
of the few positions of an ordinary tank in which riveting may be 
minimised to meet the merest necessities of fastening. The bar is 
almost invariably placed on the outer surface of the sheeting, and 
there is little or no risk of leakage. Hence there are two opposing 
courses open — one, to obtain strength and stiffness in the curb 



142 TANK CONSTRUCTION 

proper, and use as few rivets as practicable ; and the other, to utiUse 
a portion of the wall sheeting at the expense of additional riveting. 
Circumstances alone can determine which of these courses will be 
preferable in any given case, and it would be worse than useless to 
attempt to generalise on the question. 

It is almost unnecessary to point out that there is a limit to 
the amount of the wall sheeting which can be incorporated in the 
effective curb section, even with sufficient riveting to develop its 
strength. Whatever total stress is taken up by such sheeting must 
be transmitted back to the main member, in which it will set up 
shearing forces, and only so much flange stress can be developed 
as the web will stand in shear. The conditions are exactly those 
of the ordinary built-up plate girder, and detailed discussion would 
therefore be out of place here. 

With a tank rectangular on plan, it is doubtful whether the 
continuity of the top curb obtained by merely gusseting at the 
corners would be of any appreciable value. Much would depend, 
of course, upon the relative lengths of the tank sides, but if the length 
of the tank were more than i'5 times its breadth, the points of 
contraflexure in the longer span of curb would probably be so little 
removed from the ends that the maximum bending moment would 
occur at the centre of the span, and its magnitude might be but 
little less than for a similar span with the ends freely supported. 

In such cases (and where the dimensions of the tank are not so 
large as to call for truss framing to the curbs) it is probable that 
transverse ties will give the most economical arrangement. A good 
plan is to space the transverse ties, so far as may be practicable, 
with the length of curb which each tie is to support approximately 
equal to the breadth of the tank, as indicated in Fig. 75. With 
gusseted corners the loading conditions for each panel of the curb 
would then be similar to those of Fig. 74. 

Where a roof is to be provided over the tank, the transverse ties 
to the top curb may be used as part of the framing for supporting 
the roof. Methods for treating the ties in such cases will be suggested 
later. 

Some doubt may be felt as to whether the gusseting at the tank 
corners will really give continuity of the curb, seeing that the latter 
will be simply mitre-butted, and its section considerably reduced 



FRAMING FOR RECTANGULAR TANKS 



143 



by rivet -holes in the portions where the bending action appears to 
be most effective. 

It is, of course, true that one of the essential conditions of the 
continuous beam theory — viz., that the moment of inertia shall 
be constant — is violated, and that the reduction of section occurs 
where it is most objectionable according to that theory, but there 
are other factors which modify the circumstances of the case. 

At the corners of the tank, each wall must necessarily be secured 
to the adjacent wall, and thus the sheeting will be very effectively 
supported along its vertical edge. One effect of this additional 
support will be to relieve the top curb of a considerable amount of 
the loading which would otherwise be applied to it in the neighbour- 
hood of the gusseted corner connections. 





A 


a"' 

TIE ^ 


r 


'7 


b 


a"' 

TIE-^ 


/ 




u 










( 


k 




Ai 


PLAN 


' 




Ai 


) 


1 














1 



Fig. 75. 

To attempt anything approaching a comprehensive investigation 
of the problem thus presented would involve more trouble than it 
would be worth — even supposing that an accurate solution were 
practicable — but a rational consideration of the case generally will 
show that there is not much likelihood of serious deficiency in 
a curb designed on the basis of Fig. 74 and the accompanying 
argument. 

A similar question may arise with regard to those portions 
(marked A in Fig. 75) of the longer stretches of the top curb in a 
rectangular tank, where the transverse ties are connected to the 
curb. Here, however, the curb is actually continuous, and if the 
transverse tie connections be of the form illustrated at (a) in Fig. 
60, there need be no reduction in the section of the curb beyond 
that involved in riveting the bar to the wall sheeting. Moreover, 
even though some other form of connection were employed — e. g. 
such as that shown at {h) in Fig. 60 — causing a further reduction 



144 TANK CONSTRUCTION 

of section, it is probable that a curb designed on the basis suggested 

above would be sufficient, provided that the amount of wall sheeting 

assumed as forming part of the effective curb section is not excessive. 

The bending moments — or, more correctly, the restraining moments 

— at the supports of a beam with "fixed" ends only reach the 

/WL\ 
maximum magnitude of ( j on the assumption of point-reactions, 

and the bending-moment diagram shows that magnitude attained 

as a sharp cusp. A cleated or gusseted connection — such as those 

indicated in Fig. 60 — will spread the reaction, and thus tend to ease 

matters for the curb, since the bending moment at the reduced 

AV L\ 
section will be appreciably less than the ( ), on which basis, it 

is suggested, the curb may be designed. 

Clearly, if only the section of the actual bar were reckoned upon 
as forming the curb, without taking credit for any portion of the 
wall sheeting, one might feel confident that the additional strength 
due to the co-operation of the sheeting — which is not less real 
because ignored — would provide a sufficient margin to offset against 
the reduction in strength at the tie connections. 

Altogether, therefore, it would seem that it is preferable, in 
ordinary circumstances, to take no account of the wall sheeting in 
designing the curb, thus leaving the assistance — unquestionably 
real though indeterminate — rendered by the sheeting to make good 
the shortcomings of the bar brought about through practical 
manipulation. After all, if the tank be economically designed, 
both as to proportions and sheeting thicknesses, a little weight more 
or less in the top curb is not hkely to influence the total cost to any 
appreciable extent, while the advantage of having an assured 
sufficiency of strength and stiffness in the essential framing is beyond 
question. 

Where the length of the tank is such that only one or two trans- 
verse ties are necessary, a slight lengthening in the ties — due to 
elastic strain in tension — would tend to reduce the bending moment 
at the panel points, and to increase it at the middle of the panels, 
thus rendering these moments less unequal. In any case, however, 
this would be 6i extremely slight effect — no more than a mere 
tendency, in fact, — while it would be quite inappreciable in cases 



FRAMING FOR RECTANGULAR TANKS I45 

where the length of the tank is such that several transverse ties to 
the top curb are necessary. 

As a rule it is not wise to allow rivets to bear direct tension, and 
for this reason the cleats of the tie connection shown at {a) in Fig. 
6q^might well be fastened to the curb by means of bolts, instead of 
rivets as shown. Obviously, much will depend upon the circum- 
stances of a particular case in deciding whether bolts or rivets shall 
be used for this purpose. If the loading to be transmitted to the 
tie be of considerable magnitude, bolts will certainly be preferable ; 
but if the tension be comparatively small, there need be no hesitation 
to use rivets. On the question of cost there is probably nothing to 
be gained either way ; for, while bolts are almost certainly cheaper 
to fix than rivets in such cases, special marking is necessary to 
indicate the holes which are to be left unfilled for bolting, and the 
continuity of riveting is broken — both items adding to the cost of 
the work. 

The design of the transverse ties, as such, does not call for any 
particular description. Adequate accommodation for rivets at the 
connections, and the provision of sufficient stiffness to prevent 
excessive sagging, are of at least equal importance with strength 
in tension ; but the choice of a suitable section in any given case 
should not present much difficulty. 

■For connecting the tie to the curb it is well to notice that, with 
a gusset-plate — such as that shown at [b) in Fig. 60 — the reduction 
in the curb section will usually depend more upon the size of the 
rivets used than upon their number. Hence, it is better, from this 
point of view, to use a larger number of small rivets than a smaller 
number of large rivets. As a rule, two rivets will be sufficient as 
regards resistance to shearing, but it may sometimes be advisable 
to use three (or even four) rivets of less diameter instead, particularly 
if there be but little margin of strength and stiffness in the curb. 

Similar remarks apply also to the gusseted connections of the 
curb at the tank corners. Where the top curb is stiffened by means 
of trussed framing, as indicated in Figs. 63, 65, and 66, the ties and 
struts of the framing may be attached to the curb by means of 
cleats and gusset-plates. A typical detail for these connections 
is shown at (a) in Fig. 76. The connections on the inner (compres- 
sion) boom of the truss framing may be as shown at (b) in Fig. 76, 
L 



T46 TANK CONSTRUCTION 

which indicates also the attachment of the supporting props to the 
inner boom. In Fig. 64 the prop is shown attached to the inner 
face of the boom angle. This method is not infrequently used, but 
involves a somewhat complicated connection between the foot of 
the prop and the bottom curb angle. The arrangement indicated 





("plan similar 

TO (cl), EXCEPT 
FOR PROP.) 



mm^ 



STRUT 





Fig. 76. 

at {b) in Fig. 76 simphfies matters by turning the props so that the 
ordinary sheeting rivets through the bottom curb may be used to 
hold the feet of the props. 

Another method for attaching the props to the framing is shown 
at (c) in Fig. 76. With the framing arranged as indicated in Figs. 
63, 65, and 66, the shorter web members (lying at right angles with 
the booms) of the framing will be struts; they must, therefore, be 



FRAMING FOR RECTANGULAR TANKS 



147 



of angle (or other flanged) section, and the attachment of the props 
to them will do no harm if kept near the boom. 

It is because these shorter web members are struts that the 
cleats marked k in Fig. 76 are necessary, to give proper means for 
transmitting the thrusts. 

Provided that continuity be ensured, curbs and horizontal rails 
for rectangular tanks may be designed with a high degree of 
economy ; moreover, as will be seen presently, there is a particular 



B 





, 


—\ 


i 


J 


' 


> \ 




, -; 


t 


' 


r ] 


r— ^ 




1 


' ' 




■ ^ D 




!• 


















1 1 
1- 




*l 1 


1 i 


1 i 1 1 1 1 1 1 


r 






— 


c 

^^ UNIFORM PRESSURE ON CURB ? 
< I OR RAIL « Uy lb PER FOOT RUN. ^ 


> 






t 




J 








^ ' 








\ ' 








1 > 


' y 


1 ' 


< 


' > 


' ' 


• < 


' ^ 


' ' 










«; 


— ; 


- 






«. 


, 


r > 


I : 


• '^.t'l 



PLAN.— 



Fig. 77. 



ratio of length to breadth which (under favourable circumstances) 
permits a more economical curb or rail than any other proportions. 

It will be well to examine the conditions relating to such members, 
for cases frequently occur in which appreciable saving may be 
effected through taking proper account of these conditions. 

Consider the case indicated in Fig. 77, the curb or rail being 
assumed truh^ "continuous" {i.e. having the moment of inertia 
of its cross-section constant) throughout. The shorter stretches 
of the curb, having less loading applied to them from the direct 
pressure of the liquid upon the walls which they support, will not 
be able to maintain the direction of their axes at the tank corners 



148 



TANK CONSTRUCTION 



unchanged in face of the preponderating moments appUed by the 
longer stretches. The stretches of the curb or rail will deflect in 
some manner such as is indicated (with much exaggeration, of 
course) by the dotted lines in Fig. 77. 

If the curb were cut at P (Fig. 78), a couple applied to each 
of the separated ends equal to the bending moment at P (represented 
by the symbol Bp), and the stretches rebated into a straight line, 
the conditions of loading and support would be as shown in Fig. 79. 
The bending moment diagram for these conditions could be drawn 
if the magnitude of the couple Bp were known, for it will consist of 
the four parabolic curves showing the bending moments for the 
four spans with their ends all freely supported, referred to a base- 



JP S 

TtT — v: 

' ^^ POINTS OF \^ 

D / CONTRAFLEXURE-T^ 



i 



-®- 






B(C.) 



— PLAN.- — 

Fig. 78. 



line Bp below the base-line of the parabolic curves, as shown at 
{a) in Fig. 79. 

Now, the range between the sections T and V (Fig. 79) of this 
beam contains all the different stress conditions, the other ranges 
being mere repetitions. Hence, we may obtain all the necessary 
information from a consideration of this stretch. The loading to 
which the stretch T V is subjected comprises four distinct items — 
viz., (i) the couple Bb, which is the bending moment at the middle 
of the "breadth" stretches B; (2) the couple B^, which is the 
bending moment at the middle of the "length" stretches L; (3) 
the uniform loading, w lb. per foot run, due to the direct pressure 
of the liquid upon the walls supported; and (4) the support (or 
B-^L^ 
2 



reaction), w 



at Q. 



FRAMING FOR RECTANGULAR TANKS I49 

The important point to notice is that the slope of the elastic 
line at T and V will be zero. 

Regarding the end T as " built-in," the stretch T V may be 
treated as a cantilever, the slope at V being zero, and from this 
the magnitude of the couple Bl may be determined, for — 

Slope at V = 



d V 
d X 



-^=r-jr \ wl — j [ due to uniform loading ; 

= ^ - ^Xt{ ^ \~2rj (2) / ^^^ ^'^ reaction at Q ; 
^ ^~] ^l( — 2") I ^^^^ *^ couple Bl. 



d y 

d X 

w 



(B^ + 3 B2 L + 3 B L2 + L3 - 3 B3 - 3 B2 L) 



48 E I 

-2^x{B. (B + L)}. 

But this slope must be zero, and hence — 

_ ^; (L3 + 3 B L2 - 2 B3) _ 7£; (L2 + 2 B L - 2 B ^) 
^^- ^(B + L) ~ 24 



Therefore, from the diagram shown at (a) in Fig. 79 



o 24. -L^ 



Also — 



Bh = "^^ - Bp = J (3 B2 - 2 L2 + 2 B L - 2 B2) 

= -^ (B2 + 2 B L - 2 U). 

24 ^ 



If B = y^ L, the expressions for these three moments become 

1 - k + k^ 



Bp = w L2 (~ J^-^) = J» L' (Cp) ; and 

By giving to k the values o, 0*1, 0*2, ... 0*9 and i, the 



150 



TANK CONSTRUCTION 



corresponding values .of Ci,, Cp, and Cu may be calculated, as shown 
in the annexed table. 

There is obviously no need to take values of k greater than i, 



tulb PER FOOT RUN, UNIFORM >. 
Y \ 




B.iluuiiimiB 

M ^:is*— I .^HORIZONTAL 



HORIZONTAL 



h-l 



L J 



-(^) 



Fig. 79. 



for the proporfions thus represented would be mere repetitions of 
those tabulated, with L and B interchanged. If, therefore, the curb 
or rail be supposed of constant section throughout, and all bending 
moments be calculated with regard to L (the longer side), the 



FRAMING FOR RECTANGULAR TANKS 



151 



tabulated values cover the whole range of practical proportions for 
rectangular tanks. 

Where k is very small, the case represented is that of an extremely 
narrow tank. The short stretches of curb would then transmit the 
end couples from one long stretch to the other, and the long stretches 
of curb would act as though built in to a rigid anchorage at each 
end. This is shown by the tabulated values of C^, Cp, and Cb for 
k == 0, and the point is of more importance as tending to give a 
clear understanding of the facts than as likely to be of direct applica- 
bility in the practical design of tanks. 



k. 


Cl. 


O'O 


0-04167 


O'l 


0-04917 


0'2 


0-055 


0-3 


0-05917 


0-4 


0-06167 


0-5 


0-0625 


0-6 


0-06167 


07 


0-05917 


0-8 


0-055 


0-9 


0-04917 


i-o 


0-04167 



0-08333 
0-07583 

0-07 

0-06583 
0-06333 

0-0625 

0-06333 
0-06583 

0-07 

0-07583 
0-08333 



Cb. 


CpL. 


Ckb. 


- 0-08333 


0-2II 





- 0-07459 


0-186 


— 


— 0-065 


0-168 


— 


- 0-05459 


0-156 


• — 


- 0-04333 


0-149 


— 


- 0-03125 


0-146 


■ — ■ 


- 0-01833 


0-149 


• — 


— 0-00458 


0-156 


— • 


+ o-oi 


0-168 


0-323 


+ 0-02542 


0-186 


0-249 


+ 0-04167 


0-2II 


0-2II 



As the value of k increases from o to 0-5, the bending moment 
Bl increases from to — 7— ; the bending moment Bp decreases 

from to — ^ ; and the bending moment Bb decreases from 

w L^ w L 

to -, of the same kind or sense as Bp. 

12 32 

The bending-moment diagram for k = 0-5 is shown in Fig. 80. 

As k increases from 0-5 to i, Br decreases from — >" to : 

^ 16 24 

w L^ w L^ w L^ 

Bp increases from — ^ to — — ; and Bb varies from^— of the same 



16 



12 



w 



L2 



32 



sense as Bp to of the same sense as B^ , passing a point of zero 

24 

magnitude between k = 0-7 and k = O'S. 

Obviously, with k = 1 the tank is square on plan, and the 

bending-moment diagram for this case is shown in Fig, 81. 



152 



TANK CONSTRUCTION 



The value of k to give Bh = o may be determined by equating 
the expression for Be with zero, whence — 

- 2 ± V4 + 8 



^2 -j- 2 ^ — 2 = o ; .'. k = 



= (V3- I). 



Therefore, for Bb = o, the proportions are B = L (07321). 




Fig. 80. 



The points of contraflexure in the longer stretches (L) of the 
curb may be located for all values of k. In the shorter stretches 
(B) there will be no points of contraflexure unless k exceed (V^ — i). 




Fig. 81. 



For the lonsrer stretches- 



ie> X' 



= Bi, ; whence x = 1. \^2 C, , 



where x is the distance between each point of contraflexure and 



FRAMING FOR RECTANGULAR TANKS 



15: 



the centre of the span. For practical convenience it will be better 
to know the distance between the points of contraflexure and the 
tank comers ; hence : (0*5 L — %) = L (0*5 - V2 Cl). This may 
be written as L (Cpl), and the values of (Chl) corresponding to all 



005 
004 

005 










___ 














^ 


.^ 


^c. 










x. 




X 


















N 




















/ 


0C2 

001 



—O-OI 


















/ 


/ 
















Cs- 


/ 


















/ 









01 

VALUE 


02 

S OF 


03 


04 


OS 


0-6 07 

/ 


/ 0-8 


09 


I'C 


-002 














/ 








-003 












/ 


















/ 












-005 








A 


/ 












-006 






/ 


{i 






Cp 








-0-07 
-0^ 




Z 


/ 




■ 






^ 






y 


^ 














\ 


N 


-(X3e 


/ 


















s 



Fig. 82. 



values of k, calculated from this relation, are given in the table with 
Cl, Cp, and Cb in page 151. 

Similarly, for the shorter stretches, the distance between a tank 
corner and the nearer point of contraflexure will be equal to — 

V21Ch\ 



(0-5 B - L Va Cb) = B (0-5 - 



154 



TANK CONSTRUCTION 



This distance may be denoted as B (Cpn), and the vahies of (Cfb) 
corresponding to the possible values of k, calculated from this 
relation, are tabulated above with (CpiJ. 

The distances L (Citl) and B (Cpn) are indicated in Fig, 78. 

We shall now proceed to consider means by which the infor- 
mation deduced above may be turned to useful account in the 
practical design of tanks. 

As they may be of assistance in actual designing, the values of 
Cl, Cp, and Cc, as tabulated above, are shown plotted with the 



0-5 



04 



02, 



0-2 



O I 

























































A 




















cO 


V 




















\ 




^ 


















> 


^ 


\ 




^ 


c,. 










^ 































































0-4- O'S ofc 07 
VA^LUES OF K 



Fig. 83. 

corresponding values of k, giving the curves of Fig. 82. The values 
of Cpi^ and Cpn are not shown in Fig. 82, as the diagram would be 
rendered inconveniently high by their inclusion plotted to the scale 
suitable for d,, C,., and Cb ; Cpi^ and Cfb are therefore shown plotted 
separately in Fig. 83 to a more convenient scale. 

From Fig. 82 it will be clear that the proportions for rectangular 
tanks giving the least severe loading upon the curb or rail are in 
the neighbourhood of L = 2 B ; though there is but 5*33^' increase 
in the magnitude of the maximum bending moment (as compared 
with that for B .= 0-5 L) where B = 0*3 L, or B = 07 L ; and 12% 
increase where B = 0'2 L, or B = 0*8 L. 



FRAMING FOR RECTANGULAR TANKS 



155 



Now, as to the means for utilising, in practical dfesign, the 
information obtained in the foregoing investigation. 

The author would suggest that there are many cases in which 
the curb or rail might well be forged to a right-angle bend at each 
corner of the tank, and spliced at points of contraflexure. For 
instance, the curb or rail might be in four stretches, as indicated 
in Fig. 84, with splices at A, B, C, and D. The stretch A B would 
be similar to the stretch C D, and the stretch B C similar to the 
stretch D A, such similarity tending, of course, to reduce the costs 
of manufacture. 

This method would not be suitable for heavy curbs, of channel 
or other large rolled sections; but, then, such sections are very 
seldom used for top curbs or horizontal rails in tank construction, 
and are not as a rule suitable for such 
purposes. A somewhat stronger objec- 
tion is the increased difficulty in arrang- 
ing for transport to avoid damaging the 
forged bars — though this is not likely 
to be anything like so troublesome with 
rectangular tanks of ordinary sizes and 
proportions as with the curved bars and 
plates for a cylindrical tank. 

As regards cost of manufacture, the 
suggested method should compare favourably with that in common 
use ; though in this connection much would, of course, depend upon 
the resources available concerning equipment and labour. 

The splicing of the curb or rail at the points of contraflexure 
might well be effected by means of electric or other welding, for 
the wall sheeting will in all probability be sufficient to transmit 
the shearing force. It is, of course, quite possible that the curbs 
or rails might be in straight lengths, mitred and welded in position 
(by electrical or other means) at the tank corners ; but one would 
require fairly exhaustive tests, and reasonably conclusive evidence, 
before recommending the placing of full reliance upon such methods 
at the corners of a tank curb, where a failure — or even a relatively 
small loss of strength or stiffness — might lead to disastrous 
consequences. 

The attitude widely adopted towards the new forms of welding 
seems to the author unreasonable. It is similar to the attitude 




Fig. 84. 



156 TANK CONSTRUCTION 

adopted by so many engineers towards reinforced concrete, as well 
as to many other forms of construction which have been proposed. 
The question seems to be as to whether all connections shall be 
riveted, as formerly ; or all welded — just as many engineers appear 
to have difficulty in deciding whether reinforced concrete shall be 
rigorously excluded, and structures built entirely of brickwork or 
steel as formerly ; or whether all the old and tried methods of 
construction shall be swept away, leaving reinforced concrete to 
bo emplo3^ed for all structural work, regardless of its suitability — or 
otherwise. 

The results of experience generally indicate that each method 
which can be justified on appeal to fact has its own particular field 
of usefulness ; under certain types of circumstances a particular 
method is preferable to others, and under other circumstances its 
advantages are lost. And surely this is almost invariably the case 
with human beings, as well as with their productions. Why, then, 
should we demand, before admitting a suggested process, that it 
shall be capable of supplanting all others previously employed, 
and to show an improvement upon them all from every possible 
point of view ? 

There are many connections in tank work which could be readily 
made by welding ; and there are many others for which riveting is 
— and will probably remain — best in every way. The sensible 
course would seem to be the application of the most suitable method 
for each operation, instead of being tied to one process for all. Of 
course, there are difficulties ; but one so often finds that difficulties 
consist largely of inertia in those who meet them. The difficulties 
in the way of adopting new methods might frequently be moi:e 
correctly defined as difficulties in the way of arousing sufficient 
interest on the part of those concerned. 

If it be desired to arrange the curbs or rails in straight lengths, 
with riveted connections at the tank corners, the question arises 
as to what will be a suitable form of connection. 

The ordinary gusset-plate, as indicated in Fig. 73, involves a 
more or less considerable reduction in the strength of the section, 
especially at the outermost rivet-holes for the gusset-plate, where 
none of the stiffness and strength of the latter has yet been added 
to the main member. Moreover, the vertical corner angle of the 



FRAMING FOR RECTANGULAR TANKS 



157 



tank would interfere with such a connection if used for a horizontal 
rail below the brim of the tank. 

A preferable arrangement, suitable for curbs and rails alike, 
is the forged angle connection indicated in Fig. 85, or the cleated 
gusset shown in Fig. 86. The latter may be 
formed of a plate and angles, as at {a), or of 
a bent plate, as at {b), in Fig. 86. 

The forged angle connection of Fig. 85 is 
particularly suitable for curbs or rails of 
angle section. The connecting piece should 
be of the same section as the curb or rail, and 
the parts secured to the main members should 
be of sufficient length (L) to accommodate 
the rivets (or— perhaps preferably — bolts) 
necessary to transmit all the loading from the 
main member to the connecting piece. 

Similar provision is necessary with the angle cleats or plate 
flanges of the arrangement shown in Fig. 86. With this latter 
connection, the width of the gusset-plate required to accommodate 
the necessary rivets will give to the plate a considerably greater 
strength and stiffness to resist bending than that of the main curb 




Fig. 85. 




Fig. 86. 

or rail ; and this will tend to increase the bending moments at and 
near the connections. 

It may be profitable to consider, very briefly, the effects of 
variation in the section of an otherwise "continuous" member 
upon its elastic hne. Let us suppose that, if truly continuous, the 
stretch T V (see Fig. 79), under given loading, takes up the elastic 



158 



TANK CONSTRUCTION 



line indicated at (a) in Fig. 87. Now suppose a reduction in the 
section to occur over the support Q. The member will yield more 
than formerly under the bending action in (and near) the range in 
which the section is reduced; but since the contiguous portions 
must have a common slope at the point of contraflexure, the elastic 
line will be altered to some form such as that indicated at {b) in Fig. 
87, the effect being to lengthen the (quasi) freely supported spans 
between the points of contraflexure in all four wall stretches of the 
curb, and thus to increase the bending moments Bl and Bb, while 
reducing the bending moment Bp, 

If, on the other hand, the strength of the section were increased 
over the support, the member would yield less under the bending 




Fig. 87. 



action in (and near) the range in which the section is increased; 
hence, the elastic line will be altered to some form such as that 
indicated at (c) in Fig. 87, the effect being to shorten the (quasi) 
freely supported spans between the points of contraflexure, and 
thus to decrease the bending moments Bl and h^^, while increasing 
the bending moment Bp. 

Where the ratio borne by the length of the tank to its breadth 
is such that the bending moment in the curb or rail (as estimated 
on the basis described above) at the middle of the longer span is 
greater than that at the tank corners, the provision of greater stiff- 
ness and strength at the corner will tend to improve the conditions 
as regards loading. Conversely, if the tank be so proportioned that 
the maximum bending moment in the curb or rail, with true con- 
tinuity, would occur at the tank corners, the provision of increased 



FRAMING FOR RECTANGULAR TANKS 



159 



stiffness at the corners might render the straining actions at those 
parts still more severe. 

In seeking to obtain continuity for a top curb or horizontal rail 
by means of connections at the tank corners, much will depend — 
as regards the effective results — upon the "spread" of the con- 




FiG. 88. 

necting pieces across the corners. For example, with a forged angle 
connection of the type illustrated in Fig. 85, the conditions with 
the connecting piece close in to the corner, as indicated at {a) in 
Fig. 88, will be different from those with the connecting piece spread 
widely across the corner, as at (b) in Fig. 88. 

1 n u 1 1 1 11 1 u 1 1 1 1 1 1 1 1 1 1 ip ■ 



^ 



(a) 



CONNECTING PIECE AOEQUATELV 
SECURED TO EACH SPAN 



J 1 1 1 1 1 1 1 i Ui y ill 1 i 1 1 1 u 1 L 



(b) 



Fig. 



This point will, perhaps, be seen more clearly if the facts be 
considered from another point of view. 

Suppose we have two contiguous freely supported spans, both 
uniformly loaded, and having a common support, as indicated at 
(a) in Fig. 89 ; and suppose that we seek to obtain continuity over 



l60 TANK CONSTRUCTION 

the common support by means of a connecting piece, as indicated 
at (b) in the same sketch. The similarity in effect between the 
conditions for this case and those for a curb or rail at a tank corner 
will be obvious. 

It is important to notice that the bending moment in the con- 
necting piece will be constant, whereas the bending moment in the 
corresponding range of a truly continuous beam would vary from 
section to section at a high rate. 

The inferences to be drawn from this are of considerable practical 
importance, being capable of serving very useful purposes; but 
as they will doubtless be clearly apparent upon consideration, there 
seems to be no need for elaboration here. It will be found both 
interesting and instructive to investigate the elastic lines for curbs 
or rails connected in this manner, with different degrees of " spread " 
for the connecting pieces ; and this is commended to the careful 
attention of the reader. 

Two points should, however, be observed before passing on; 
viz. — 

1. That, unless the tank be square on plan (or the curb 
stayed in equal panels on all walls), the bending moments in 
adjacent spans — assuming true continuity, and, of course, uniform 
loading throughout — are not symmetrical about the tank corners ; 
and 

2. That the rivets or bolts which secure the connecting pieces 
to the main members of the curb or rail should be capable of 
developing the strength of the connecting pieces, which will usually 
be more than that of the main members themselves. 

It is probable that, in ordinary circumstances, the preferable 
course is to give the connecting pieces no more spread than will 
provide reasonable facility for the inspection, scaling, and painting 
of all surfaces, both of the connecting pieces and of the other con- 
structional members in the vicinity. At the same time, however, 
instances may frequently occur in which an appreciable saving 
may be effected in the main curb or rail members through the 
exercise of a little care and thought in arranging the connecting 
pieces with a suitable spread ; and such opportunities should certainly 
not be missed. 

There is yet another method, which may be useful in many 



FRAMING FOR RECTANGULAR TANKS 



l6l 



cases, for advantageously connecting the curbs or rails at the corners 
of a rectangular tank. This method is indicated in Fig. 90. from 
which the underlying principles will be clear. 

The arrangement shown at {a) is suitable for tanks square or 
nearly square on plan; and the arrangement at (b) for tanks in 
^S/'hich the breadth is so small in comparison with the length that 
the shorter stretches of the curb or rail need no support other than 
that which can be afforded them at their ends by their attachment 
to the vertical corner angles of the tank. 

Obviously, a combination of the two forms may prove con- 
venient in some instances ; and in others the arrangement shown 
at [b) in Fig. 90 may be used for both pairs of walls. 




(b) 



TIE 



J' 



K° 



Fig. 90. 



This method has a distinct advantage in that the curb or rail 
members need not be spliced, while the simply splayed ends may 
be made to present a very good appearance. 

By suitably placing the ties in either arrangement, the ends 
of the curb or rail may be made to press lightly inwards against 
the vertical corner angles, thus reducing the more or less common 
tendency to leaking at the tank corners. 

The ties are regarded as acting in tension only, and hence neither 
the ties nor their connections with the main members need be 
provided with stiffness to resist bending actions other than those 
due to the weight of the ties themselves. 

A detail suitable for use with the arrangement shown at (a) in 
Fig. 90 is shown in Fig. 91, and it will be seen that no reduction 
in the strength of the main members is caused by this form of 

M 



l62 



TANK CONSTRUCTION 



•connection. For the arrangement shown at (b) the details given in 
Fig. 60 for ordinary transverse ties will be suitable. 

The conditions as regards loading in the curb or rail members 
will perhaps be clear from the following consideration — 

With the arrangement shown at [a) in Fig. 90, suppose each of 
the ties to be replaced by a flexible but inextensible cord, passing 



3 X. ^ F UAT T I E. 




7" 

^ DiA t?ivET5 



Q^x'bV'^L. 



\-r^-<'"r-rr- i 



12 



z 



Fig. 91. 



Fig. 92. 



over a frictionless and adequately supported pulley, as indicated 
in Fig. 92. From this it is an easy step to the loading diagram of 
Fig. 93, and a simple basis for designs readily suggests itself. In 
the longer spans (and also in the shorter if the breadth of the tank 
be not much less than its length) there will be a point of zero slope 



^ 



■^ 



■^ 



^1 1 Ul 1 1^11 Ul 11111 111 11 UllUllUlilj 



p 



Fig. 93. 



somewhere between the tie-connection and the tank corner — a 
section at which the conditions resemble those of a "built-in" 
end. The exact location of this section will depend upon the cir- 
cumstances of each case — and, in particular, upon the ratio borne 
by the length of the tank to its breadth. A little consideration 
will show that all practical requirements should be satisfied if the 
members be designed for a maximum bending moment equal to 



FRAMING FOR RECTANGULAR TANKS 163 

W L\ .11 

J, where W is the total pressure acting upon the longer 

stretch, and L the full length of the tank. The same section should, 
of course, be used for the shorter as for the longer spans. 

The tension in the tie may be estimated for designing by taking 

the bending moment ( j, and dividing by D (Fig. 90), the 

distance between the tie-connection and the tank corner — taken 
rather on the small side for preference. The quotient will, of 
course, be the magnitude of each force of a couple having the arm 

D, and of magnitude equal to ( j. Add to this force one-half 

of the total pressure ( i. e. — ) acting upon the longer spans of the 

curb or rail, and the resulting sum will be the total effective force 
normal to the longer wall of the tank, to be resisted by the tie. 
This total force, resolved to the angle of the tie, will give the load 
for which the tie and its connections should be designed, with any 
additional margin which may be considered desirable. Expressed 
symbolically, the tension in the tie will be — 

1 = — ^ -\ cosec a 

\I2 D 2 / 

„. /L + 6 D 
= W cosec a :p. — 

\ 12 D 

The additional tension in the main members between the ties, 
due to the inclination of the latter, should not be forgotten when 
employing the arrangement {a) of Fig. 90. 

For the arrangement (b) the treatment follows simply and 
obviously from the foregoing discussion. 

Convenient modifications of this method will doubtless present 
themselves, and as the object here is to be broadly suggestive 
rather than exhaustive, the matter may be left without further 
elaboration. 

The application of the corner connections indicated in Figs. 85 
and 86 to curbs and rails provided with transverse ties or trussing 
(or both) will be obvious ; and it will also be clear that corner 
splicings may be rendered unnecessary with such curbs and rails 



164 TANK CONSTRUCTION 

by suitably arranging the ties or trussing-panels on the lines 
indicated above in the discussion relating to the suggested method 
of Fig. 90. 

Where two lengths of a curb or rail meet, the butt or mitre 
should be spliced with covers on all sides — even though such covers 
may not be necessary for purposes of strength — as a protection 
against corrosion. The advantage possessed by the arrangement 
of Fig. 90 in this respect is worthy of particular notice, as not only 
is the cost of the splicings saved, but all the surfaces are freely open 
for inspection, scaling, and painting. 

It will probably have been noticed that, even with true con- 
tinuity in a top curb or horizontal rail, if the tank be not square 
on plan (or the stretches stayed in equal panels on all walls) there 
will be a twisting action upon the vertical corner angles which no 
amount of gusseting or connection between the members can prevent. 
This twisting action is, of course, small with well-designed curbs 
and connections, but in many cases it is better avoided, since it 
provides an additional tendency to cause leaking by the opening 
of the seams between the corner angles and the wall sheeting. A 
small leak may soon become so large as to be serious ; and a leak 
in a tank — particularly at a corner — once started, is often both 
troublesome and costly to remedy. The obvious course to avoid 
such twisting actions is to stay the curbs or rails in equal panels on 
all walls. 

Where vertical stiffeners are used, they should (for the reasons 
given in pp. 127-130) be placed on the outside of the tank walls. 
Whether they be placed outside or in, however, the problem of 
their fitting and attachment to the top and bottom curbs is, 
apparently, much the same. If placed inside, according to the 
common arrangement shown in Fig. 57, each stiffener may be either 
joggled into the bottom curb or packed off the wall sheeting. If 
placed outside, as indicated at {b) in Fig. 59, it would seem that 
each stiffener may be either joggled into the top curb or packed off 
the wall sheeting. 

No useful purpose would be served by entering into the old 
controversy as to the respective merits of joggling and packing. 
So much depends upon the equipment available (or, more commonly, 
lacking) in particular yards and shops, and so much upon personal 



FRAMING FOR RECTANGULAR TANKS 



165 



Tl 









212" 



prejudice and inertia, that there seems httle hkehhood of an impartial 
comparison doing aught but raise a storm of protest. 

There is, however, another method, which the author would 
suggest as being, perhaps, at once cheaper and more simple than 
either packing or joggling, while leaving no inaccessible pockets 
in which corrosion may go on undetected. This suggested method 
is shown in Fig. 94, and should need no further description. The 
dimensions given in the sketch should provide sufficient strength 
for all ordinary cases in which the use of vertical stiffeners can be 
reasonably justified, but there should be little 
difficulty in securing greater strength if desired. 
As has been stated already, the author is of 
opinion that vertical stiffeners— of this type, at 
least — should not be employed if any other 
method be available. 

44. Continuity of Sheeting. — As regards con- 
tinuity in the sheeting where vertical stiffeners 
are used on the outside of the walls with only 
light tack-riveting, it is probable that the most 
satisfactory results are to be obtained by using 
the thinnest sheeting practicable, spacing the 
stiffeners on the assumed basis of true continuity 
in the sheeting, and allowing only a half-width 
panel of sheeting at each end of every wall. 

Where a vertical seam in the sheeting is necessary, it is the 
common practice to locate the seam at a stiffener, using for the 
latter a fairly broad-tabled tee (instead of an angle, as elsewhere) 
to form one cover for the butt of the sheeting, with a cover strip 
on the other side. This does not seem a proper thing to do at a 
section where the bending moment in the sheeting is apparently 
at its maximum — particularly as close riveting is essential to prevent 
leaking, and the section of the sheeting is considerably reduced in 
consequence. However, in view of the fact that trouble seldom 
arises from this cause, there would appear to be little ground for 
adverse criticism of the practice. The arguments given in pp. 157- 
159 regarding the probable behaviour of an otherwise continuous 
curb or rail weakened over a support, will, presumably, apply 
equally to sheeting ; and hence it may be that the various portions 



ANGLE, OF 
SAME SECTION 
AS VERTICAL 
STIFFENED. 



^ 



Fig. 94. 



i66 



TANK CONSTRUCTION 



of the sheeting form among themselves some mutually satisfactory 
arrangement for sharing the load on a basis of give-and-take, working 
together amicably upon that basis. If so, it is to be regretted that 
their example is not more generally followed among their human 
acquaintance. 



C 



t 



7 



A 



=^ 



ROOF BEAM 



(SIDE SUPPORT SIDE SUPPORT,. 

^ at) ^ 



\: 



FLOOR JOIST 



z 



y 



K 



^. 



IE 



>a 



; 



SIDE SUPPORT 



SIDE SUPPORT 



(h) 



L 



FLOOR JOIST 



V^ 



V 



^ 



Fig. 95. 

45. Ribbed Tanks. — In tanks of large depth the wall sheeting 
may be supported by vertical members continuous with the floor 
supports. The vertical supports may also have free support — by 
means of transverse ties or an adequate curb — at the brim or some 
lower level ; or they may be made continuous with transverse beams 
carrying the roof. Two such cases arc indicated in Fig. 95. 



FRAMING FOR RECTANGULAR TANKS 



167 



Now, it will be clear that unless the tank be kept full, so that the 
contained liquid is in contact with the underside of the roof, the 
assistance rendered to the side supports by a roof beam continuous 
with them cannot amount to much. Indeed, it is quite possible 
for a roof beam continuous with the side supports to increase — 
instead of diminishing — the loading upon the side supports. Even 
with the contained liquid subjected to a superimposed pressure, the 
conditions are not much improved, for the superimposed pressure 
will be transmitted to the side supports and floor beam by the 
contained liquid. The weight of the roof beam, and the roof 
construction and loading which it supports, cause the same kind of 



FLOOR- 



. T-i-.. 



to) 



mnxn 



^jiLA i z X. R 



ROOF- 



•p a 



FLOOR 



(b) 



ROOF - 



Fig. 96. 



flexure in the continuous beam as does the outward pressure of the 
contained liquid acting upon the side supports, and this is the reason 
why such methods are not to be recommended for practical use. 

Consider the supports indicated at (a) in Fig. 95 ; and imagine 
them cut at the corner P and rebated to form a straight continuous 
piece, as indicated at (a) in Fig. 96. With the contained liquid not 
quite (but very nearly) filling the tank, the loading on this straight 
member would be as indicated at {a) in Fig. 96, and the continuity 
couples at P are shown applied as external couples at each of the 
cut ends. 

The weight supported by the roof beam Q R becomes an upward 
pressure in the straight piece of Fig. 96, and causes flexure of the 
same kind as does the direct loading upon the side walls. 

Now suppose the tank to be full, and the contained liquid 



1 68 TANK CONSTRUCTION 

subjected to a superimposed pressure of such magnitude that the 
upward pressure apphed to the roof 'beam is just sufficient to nuUify 
the weight of the beam and the roof (downward) loading which it 
supports. The loading upon the straight piece would then be as 
indicated at (b) in Fig. 96 — the roof beam O R free from loading, 
but the loading on the side supports and floor bearer correspondingly 
increased. 

The stiffness of the roof stretch Q R would, of course, act as a 
restraint against further flexure of the side supports after the roof 
stretch had taken its flexure due to its own loading ; but in that 
process the side supports would have been subjected to flexure by 
reason of their continuity with the roof stretch. 

In the rare case of a tank in which the contained liquid is always 
subjected to a considerable superimposed pressure, there is more 
ground for making the roof beam continuous with the side supports ; 
but the strongest reason for adopting the method in such a case is 
that it provides a ready means of meeting the necessity for tightness 
against leakage along the junctions of the side walls with the roof, 
and not so much because it promises advantage (as regards saving 
of material) from continuity effects. 

For an ordinary storage tank a good deal will depend (as regards 
the assistance rendered to the side supports by a roof beam con- 
tinuous with them) upon the proportions of the tank. Assuming 
true continuity in the frame (the section constant throughout all 
the four stretches), the side supports would receive much more 
assistance from the roof beam in a tank of small breadth and great 
depth than it would in a tank of great breadth and small depth. 
The more favourable case seldom occurs in practice, however ; and 
it is doubtful whether the advantages to be gained are worth the 
trouble in any ordinary circumstances. It is probable that an 
effective tie, with ordinary connections, will generally be found 
preferable, from all points of view, to a roof beam continuous with 
the side supports. 

With regard to continuity between the floor joist and the side 
supports, since the direct pressures upon these stretches tend to 
cause opposite kinds of flexure, it is obvious that continuity will be 
advantageous, provided that an effective and economical means for 
securing it be employed. 



FRAMING FOR RECTANGULAR TANKS 



169 



The most satisfactory way of obtaining such continuity (were 
it not for practical difficulties) would be by forming the side supports 
and floor joist of each " bent" in one piece; and this method has 
been used for tanks constructed of reinforced concrete. Rolled 
steel joists and channels, however, cannot be bent — even to a fairly 
flat curve — without a great deal of trouble and considerable loss of 
strength. 

46. Use of Raking Stays. — From the discussion relating to con- 
tinuit}/ at tank corners for curbs and horizontal rails (pp. 157-159) 
it will be clear that little real success is likely to attend any effort 
to obtain continuity for the bent in separate stretches, by means 
of gussets, fishplates, and flange covers, for the section would 



(U) 




RAKING STAYS 




(h) 



-4> 4 

Fig. 97. 




inevitably suffer more or less considerable reduction in parts due 
to the rivet holes. 

Probably the best method, from the practical point of view, 
is to merely prevent horizontal movement at the feet of the vertical 
supports by cleating them adequately to the floor joists, and making 
no attempt to provide resistance to bending in the cleats. The 
overturning action on the side supports may then be taken up by 
raking stays secured to the floor joists, as indicated at (a) in Fig. 
97 ; or by a transverse tie as at (b) in the same sketch. 

It will be seen that the raking stays make for economy in one 
direction — the outward pressure of the contained liquid on the side 
supports is applied to the floor joist as an upward lifting tendency, 
and advantage may be taken of this in designing the floor joists and 
the steelwork or other construction supporting them. The arrange- 
ment shown at (b) in Fig. 97 does not give this additional economy ; 



1 70 TANK CONSTRUCTION 

but, on the other hand, this latter arrangement involves only one- 
half the number of connections necessary for the raking stays. 
Moreover, by reason of the incUnation of the raking stays, the con- 
nections for the arrangement (a) will be subjected to more severe 
loading than those for the arrangement (b) — circumstances being 
similar for both, of course ; and the bracket action of the raking 
stays in the arrangement (a) will set up compression in the lower 
ranges of the side supports. With reasonable care in designing, 
however, and under ordinary circumstances, these compressions 
need never assume such magnitudes as to require special provision in 
the members for their proper transmission. 

The action of the raking stays will set up a tension in the portion 
of the floor joist between their feet, and a few remarks with regard 
to this are necessary, since the action may be turned to useful 
account. 

The outward pulls being apphed to the top flange of the joist, 
a bending action will be induced, tending to raise the middle portion 
and depress the ends — i. e. a bending action of the opposite sense 
from that caused by the weight of the contained liquid. Owing to 
the fact that part of the tension will be taken by the floor plating, 
it is difficult (as well as inadvisable) to attempt anything approaching 
a definite estimate as to the magnitude of this reverse bending 
action, which may be generally reckoned upon as reducing the 
stresses in the floor joist due to the direct loading on the tank floor. 
The best course will be for the designer to treat each case upon its 
merits, and with a proper regard for its particular conditions and 
circumstances, remembering that while every legitimate endeavour 
should be made to prevent waste of any kind, excessive " cutting" 
of the floor bearers or side supports is likely to produce a leaky tank, 
through opening of the seams in the sheeting. 

Where desirable, the effect of the reverse bending action upon 
the floor joist may be adjusted to harmonise with other factors; 
and this may be done by suitably placing the raking stays, and also 
by arrangement of the connections at their feet. The variations 
which may be obtained in the axial load taken by the raking stay 
will be seen presently, when we shall discuss the treatment for 
designing — including the most effective disposal of the raking stays. 
The influence of the connection we may investigate now. 



FRAMING FOR RECTANGULAR TANKS 



171 



Consider the detail of Fig. 98. The axial load F in the stay acts 
upon the cleats in the line A F ; and were they not prevented from 
so doing, the cleats would move in the direction A F. Opposition 
to such motion is provided by the rivets S ; and, assuming that all 
the rivets participate equally in providing the resistance, both 
horizontally and vertically, the resultant resistance to vertical 
motion of the cleats will act in the line B B. At the point in which 
B B intersects the bottom surface of the cleats, the horizontal 
resistance Rh and the vertical resistance Ry will be compounded to 
form the resultant resistance R, acting parallel with F. The con- 
nection is, therefore, subjected to an overturning action of magnitude 




Fig. 



(F @ 8) ; and the reverse bending action applied to the floor beam 
is(F@ A). 

Another way of regarding the matter is as follows. At the 
point in which B B intersects A F, the force F will be resolved into 
its two components H and V, as indicated in Fig. 98. The over- 
turning moment on the cleat, therefore, will be {R @ d) ; and the 
reverse bending moment applied to the floor joist will be (H @ D). 
Clearly, the result is the same with either line of argument. 

It is scarcely necessary to point out that the rivets S must be 
capable of transmitting the overturning moment (F @ 8) to the 
tloor beam, as well as the vertical and horizontal components of 
the force F. 

Should it be desired to increase the overturning moment on the 



172 



TANK CONSTRUCTION 



cleats without altering the force F in either magnitude or position, 
it is only necessary to modify the cleats in such a manner that the 
rivets S may be rearranged so that the line B B (in which their 
resultant resistance to vertical motion of the cleats may be supposed 
to act) shall intersect the line A F higher up the rake of the stay. 
A contrar}^ course will reduce the leverage D ; until, in the limit, 
the arrangement of Fig. 99 is obtained. In this case, 8 being zero, 
the cleats are free from overturning moment ; and the reverse 
bending moment applied to the floor joist is (F @ D), the leverage 
D being one-half the depth of the floor beam. 

It will be obvious that this means of adjustment should be used 
very sparingly, and with the utmost discretion. It may be found 
useful in cases where the loading on the floor joist would otherwise 



RAKING STAY 





Fig. 99. 



Fig. 100. 



be such that some particularly convenient section falls short of the 
requirements by a small deficit. 

Whatever proportion of the tension due to the raking stays 
may be decided upon, in a given case, as applicable to the floor 
joist, the estimated maximum stress in the joist should include the 
contributory stresses from all three sources of loading — viz., the 
weight of the liquid supported ; the appropriated tension (regarded 
as spread uniformly over the cross-section) ; and the reverse bending 
action. The tension will affect only the portion of the joist between 
the feet of the raking stays ; but the effect of the reverse bending 
action will extend beyond them, into the outer ranges. 

For the sake of clearness, the floor sheeting is not shown in 
Fig. 98. Its effect upon the inferences deduced will, however, be 
obvious. 

The total weight to be supported by the substructure will, of 
course, be unaffected by any reverse bending action in the floor 



FRAMING FOR RECTANGULAR TANKS 



173 



7 



HORIZONTAL TIE 



VERTICAL SUPP0RT>5 



joists; but the incidence and distribution of the loading may be 
varied, and this is sometimes a matter of great convenience in 
practical arrangement. 

In some cases the feet of the raking stays may be secured to a 
single pair of cleats for connection with the floor joist, as indicated 
in Fig. 100 ; and in such an arrangement neither the tension due 
to the raking stays, nor the otherwise consequent reverse bending 
action, will be applied to the floor joist. 

Such connections should always be made by means of a pair 
of cleats — either of angle bar, or of bent plates if more convenient. 
The wringing action which is 
inevitable with a single cleat !>: 
should be a sufficient argument 
against such connections, unless 
the force F be small — in which 
case it is probable that some 
other form of construction for 
the tank would be more efficient 
than that under discussion. 

47. Action of Raking Stays. — 
For depths not very great, a single 
raking stay, suitably placed, will 
provide all the support required, 
and then the top curb becomes 
unnecessary so far as regards the 

stability and stiffness of the wall yig. 10 i. 

framing. 

The treatment already given in the discussion concerning wall 
sheeting, supported solely by the bottom curb and a horizontal 
rail, ^vill apply equally, in principle, to the vertical supports of the 
arrangement now under discussion ; and the determination of the 
inost effective position for the horizontal rail will serve also for the 
attachment of the raking stays to the vertical supports. Hence, 
the designs of the supports, stays, and connections for this case will 
be a simple matter needing no further elaboration here. 

For the greatest depths likely to be required in ordinary tank 
work, provided the width be not very great, it is probable that a 
single raking stay in combination with a tie at the brim, as indicated 




RAKING 5TAV5 




174 



TANK CONSTRUCTION 



in Fig. loi, will provide the most economical and satisfactory 
arrangement. 

In such circumstances the loading conditions with regard to 
the vertical support will be as indicated in Fig. 102 ; and the bending 




Fig. 102. 



actions in the vertical support, as well as the loading to be trans- 
mitted by the raking and horizontal stays and their connections, 
may be estimated from a consideration of the elastic line of the 
vertical support, employing the usual assumptions. 



8 ^!— 'L 
i < -f 
a o 

•r l!_ 



y 4 ■/ y t V 



<' >: " 



f 



J[_jj[, 






1 



Fig. 103. 



The points A, B, and C in Fig. 102 might reasonably be assumed 
to remain in line throughout the elastic deformations, and it is 

evident that, if h be anything less than (say) —, there will be no 

4 
points of contraflexure between A and C, while a point of zero slope 

will occur somewhere about the middle of that range. 



FRAMING FOR RECTANGULAR TANKS I75 

Clearly, then, if it be granted as a prerequisite that h shall be 

always about (or less than) — , we may assume that the conditions 

will be sensibly equivalent, as regards loading effects, to those of 
Fig. 103. The investigation will be simplified by the adoption of 
this basis, while any consequent error in the results will be relatively 
small, and on the side of safety. 

Referring to Fig. 103, let p represent the maximum intensity 
of pressure per inch run of the vertical support. Then, if S be the 
distance between adjacent vertical supports, in inches ; H the total 
height of the wall, in inches ; and w the weight of the contained 
liquid per cubic inch ; — p =: ze^ H S. The total pressure on the full 

range A B will bef^jH — '^ 



2/ \ 2 

First consider the deflection of the piece A B as a simple 
cantilever, subjected to the liquid pressures, fixed in position 
and direction at A, and without support at B. 

At the section X, distant x from B, the loading intensity — 

oc \ . ( X 



and the total pressure on the range X B — 



w x^\ ( w x'^^ 

X = 



2 / \ 2 

The bending moment at X will be — 

w x^ S\ X w x^ S 



B, 



But 



2 / 3 

d^y_ B 
d x^~Er 



J 1 d^ y w x^ S z£; S , „, 

and hence— -^ = = -^^=r^ {x^). 

d x^ 6EI 6EI^' 



Integrating with respect to x- 



d y _ w S 
d X ~~ 6 E 



176 TANK CONSTRUCTION 

Since ^ = when a; = H, it follows that C = — — ; and 
ax ^4 

hence — 

dy _ jw^ /^ _ H* A - ^S _ 

^^~6ElV4 4/ 24 EI ^ ^^• 

Integrating again with respect to x — 

w S fx^ 



y 



~-^'x + C2). 



24 E I V5 
Since y = o when a; = H, it follows that 

Co - H^ - ^ = ^^) 
' 5 5 

and hence — 

wS fx^ TT4 , 4 H^ 

24 E I V 5 5 

= ~ '^4-T (4 H^ - 5 H^ ^ + x^). 
120 E I ^^ ^ ' 

At B, where x = — 

120 E I ^ • '^ 30 E I 

If the point B is to remain fixed as to position, the upward 
deflection which would be produced by a concentrated upward 
load at B equal in magnitude to the reaction Rg must be equal to 
that produced by the liquid pressures acting alone. Hence — 

Rb JP IV SH5 ^ 
3 E I ~ 30 E I ' 

ze^ S H^ 

whence — Rb = • 

10 

Thus, Rn is equal to one-fifth, and R.v to the remaining four-fifths, 
of the total liquid pressure on the vertical support A B. 
The bending moment at X, therefore, will be — 

^ _w x^ S T? _w x^ S w}!- S X 
---||(5^^-3H2^). 



FRAMING FOR RECTANGULAR TANKS I77 

Differentiating with respect to x — 

-y— = (15 x^ — 3 H2 ; 

which gives the position of maximum negative bending moment ; 
for -J — = o when (15 a;^ — 3 H^) = o ; i. e. when 15 ^^ = 2 H^; 

whence x^ = - ; and — 
5 

a; = H V J = ^^ - 0-4472 H. 

The magnitude of the maximum negative bending moment, 
therefore, will be — 

B„„ = ^ { % (5 ^ ^ - 3 H^) } 



§{5^5(H._3H'-)} 

(2H2) 

= — 0*0298 w IP S. 



wSfilVs 



30 I 5 



75 
The positive bending moment at A will be — 

Ba = ^ (5 H3 - 3 H3) =z !^J5!_§ _ 4. 0-0667 wK^S; 

and this, clearly, is the greatest bending moment in the vertical 
support. 

Should the elastic deformations in the raking stay and its 
connections permit a slight change of slope at A, the bending 
moment at A will be reduced, and the negative bending moment 
will be increased. With ordinary care in design, manufacture, 
and fitting, however, such movement as is likely to occur in practice 
should reduce the maximum stresses in the vertical supports. 

Assuming zero slope at A, there will be a point of contraflexure 
where (5 Xq^ — 3 H^ ;^q) = o ; i. e. where ^ Xq^ = ^ H^ Xq ; whence 

Xq^ = ^^-~-, and— 

5 

Xo = R V| = — ^— ^ = 0-7746 H. 

N 



178 



TANK CONSTRUCTION 



Substituting k H for x, the equation for the bending moment 
may be written — 



= z. H3 S I ^ <5 ^' - 3) I 
I 30 J 

This may be written as — 



(5 ^' - 3 k) 




Fig. 104. 

where Q = [ ^ ^^ | ; and giving to k the values 0, O'l, 

0'2, . . . 0-9, and I'o, the corresponding values of the factor Q 
may be calculated, as in the accompanying table. 

These corresponding values of k and Q may be plotted to give 
the diagram of Fig. 104, which will be found useful in practical 
design. 

The raking stay and its connections should be designed to 
transmit a tensile load of — 

T=:(r, + ^^^) sec.^, 

where is the angle (see Fig. 10 1) between the raking stay and the 
floor joist. 



FRAMING FOR RECTANGULAR TANKS 



179 



k. 


Q. 


k. 


Q. 








0-6 


— 0-0240 


O'l 


— o'oogS 


0-7 


— 0-0128 


0'2 


— 0-0187 


0-8 


+ 0-0053 


0-3 


— 0-0255 


0-9 


+ 0-0315 


0-4 


— 0-0293 


i-o 


+ 0-0667 


o'5 


— 0-0292 







Raking stays of the type under discussion should be indined 
at 45° with the floor. At any greater angle the stay and its con- 
nections will be more severely loaded; and at any less angle the 
upward lifting action upon the floor joist will be reduced. 

It should not be forgotten that the action of the raking stay 
will set up an additional compression in the portion of the vertical 
support marked A C in Figs. 10 1 and 102. As a rule this added 
compression will not form a serious item in the maximum stress in 
the vertical support ; the wall sheeting may be relied upon to prevent 
sideway flexure in the support, and hence the latter may be designed 
for a permissible stress of 7*5 tons per sq. in. Cases may arise, 
however, in which provision for the additional compression is 
necessary or advisable ; and for this reason its existence should not 
be ignored. 

As regards the arrangement of the sheeting for this class of 
wall framing, it will be noticed that the vertical supports may be 
placed outside the sheeting, thus securing at once the most effective 
means of support for the sheeting and the minimum of necessary 
riveting ; for the rivets securing the sheeting to its supports have 
no loading to transmit, and need therefore be only capable of holding 
the pieces in their proper relative positions and preventing the 
ingress of moisture and other corrosive agents between the sheeting 
and its supports. Such rivets may usually be | in. diameter, and 
the pitch about (though it should not exceed) sixteen times the 
thickness of the sheeting. 

The sheeting may usually be laid in horizontal strakes, a fairly 
light angle sufficing for the bottom curb to connect the wall and 
floor sheeting. Where the depth is sufficient to render such a 
proceeding worth while, the thickness of the sheeting may be reduced 
in the upper strakes. The strakes should be arranged alternateh' 



l8o TANK CONSTRUCTION 

"outer" and "inner" from the lowermost; and the horizontal 
seams may be single-riveted lap joints, with a packing strip inserted 
between the inner strakes and the vertical supports. "Where the 
thickness of the sheeting is reduced, however, thin packing strips 
will be necessary even for the outer strakes above the first reduction 
in thickness, and for this, as well as for other reasons, it is open to 
question whether reduction of the plate thickness really pays in 
ordinary circumstances. 

Where the length of the tank is so great that vertical seams are 
unavoidable, these seams should be single-riveted double-covered 
butt joints, and may be arranged to occur at a vertical support. 
For obvious reasons, the vertical seam in any strake should not 
occur immediately over that in the next strake below. 

The sheeting may be designed as continuous over the vertical 
supports if these latter be spaced as described for ordinary vertical 
stiffeners supported by top and bottom curbs. 

It has been assumed, so far, that the raking stays will lie in a 
verticle plane with the floor joist; but on one pair of opposite 
walls this will not be so. A suitable connection for the foot of the 
raking stay in such cases may be obtained by adequately riveting 
a short piece of joist (of the same section as the floor joists) to the 
floor plates and to the beams — if these latter lie conveniently ; if 
not, the best plan is to insert trimmer joists between adjacent floor 
j oists, to which they should be firmly cleated. The feet of the raking 
stays may then be secured to these trimmer joists through the floor 
plates. 

Other methods of staying and supporting the side walls of 
rectangular tanks will doubtless suggest themselves ; but as most 
of these will be either combinations or modifications of those 
suggested in this and the preceding chapters, there seems to be no 
need to particularise here with regard to them. 

48. Bottom Corner Connections. — The arrangement of the bottom 
curb angles at the tank corners, and the junction of these with the 
verticle corner angles, sometimes causes unnecessary difficulty ; 
and carelessness in this respect is a fruitful source of leaks at tank 
corners. A simple and sound rule is to make the bottom curb 
angle of thickness ^ in. more than the wall or floor sheeting ; while 
the width of the limbs need be no more than will suffice to accom- 



FRAMING FOR RECTANGULAR TANKS 



l8l 




SECT lONAL ELEVATION 



modate the necessary rivets for strength and for securing tightness 
against leaking. The verticle corner angle may conveniently be 
of the same section as the bottom curb ; at least its thickness should 
be the same, though in some cases the width of its limbs may be 
slightly less. 

One of the most important requirements is support for the 
meeting plates, so that the edges may be adequately caulked through- 
out their lengths ; and this may be secured by mitring the curb 
angles, as indicated in Fig. 105, the vertical corner angle fitting 
closely against the top flange of the curb angle. The mitre of the 
curb angles may be well caulked, and the square edges of the vertical 
corner angle dressed down over the rounded 
edge of the curb angle, to prevent the 
ingress of water into these small spaces. 
The author is of opinion that this is an 
instance where electric or flame welding 
might be employed with advantage ; it 
would certainly provide a more effective 
barrier against corrosion, and also greater 
stiffness for the caulking of the plate and 
angle edges. The only drawback is the 
cost— at present so high as to be pro- 
hibitive for most ordinary work — but 
perhaps that may become more rational 
in the future. 

Before leaving the subject of the connection in which the vertical 
corner angle meets the bottom curbs of two adjacent walls in an 
ordinary rectangular tank, it may be well to notice a form which 
has been widely used for many years. 

A three-way corner piece is formed, as indicated in Fig. 106, 
with the limbs of sections to match the corner angle and curbs. At 
one time, it is believed, these corner pieces were cast in steel ; but 
latterly they have been much more commonly forged from the 
ordinary stock angle sections. The ends of the limbs are finished 
square, and are butted closely to the ends of the corner angle and 
curbs, each butt being covered on the inside with a round-backed 
cover strip of bent plate, accommodating three or more rivets on 
each side of the butt. 



BOTTOM CURB ANGlE.5, 

SECTIONAL PLAM 
Fig. 105. 




l82 



TANK CONSTRUCTION 



Clearly, it would be difficult and costly to cover the joints of 
the angles with the detail shown in Fig. 105, and in this respect the 
forged connecting piece of Fig. 106 has the advantage. In cases 
where electric or flame welding is not available, therefore, some 
such detail as that indicated in Fig. 106 may be preferable to that 
of Fig. 105 ; but the forging and fitting involved with the three-way 
corner piece are obviously expensive, and the butt strips cannot 
cover the joints of the angles completely. 




Fig. 106. 



Another method which is sometimes (and perhaps frequently) 
used is to forge a corner connecting piece (two-way) for the bottom 
curbs only, butting and covering where the main curb angles meet 
the connecting piece. The vertical corner angle is then joggled to 
rest inside the angle of the corner piece, and the inevitable pocket 
spaces formed by the joggling along the top edges of the corner 
piece are " plugged" — which, being interpreted, usually means that 
they are more or less filled with some kind of putty or cement. This 
method cannot be recommended, for the cost of joggling and plug- 
ging, added to that of the forged two-way connecting piece, makes 
the total outlay but little (if at all) less than that for the three-way 
connecting piece of Fig. 106, while its disadvantages are obvious. 



CHAPTER VI 



TROUGH-BOTTOMED RECTANGULAR TANKS 

49. Action of a Trough Bottom. — ^The question of trough bottoms 
for rectangular tanks has already been considered in Chapter II, 
so far as regards the effects of cross-sectional shape and proportions 
upon the economy of sheeting area for specified contents. We 
shall here discuss the trough-bottomed rectangular tank from the 
standpoint of practical design, 
both for strength and con- 
venient arrangement. 

First, let us examine the 
facts as regards loading for a 
typical case. In Fig. 107 the 
cross-section of such a tank is 
indicated, the trough being 
semi-elliptical, and its capacity 
about 25 per cent, more than 
that of the rectangular portion. 
The vertical side walls are 
assumed to act as longitudinal 
girders supporting the whole 
weight of the tank and its con- 
tents, they themselves being 
supported upon stanchions or 
other construction. 




Fig. 107. 



Confining our attention for the moment to the trough, let us 
imagine the skin composed of a number of links, sensibly rigid 
in themselves, but connected by means of frictionless hinges. We 
may then regard all the liquid pressures between the middle points 
of any contiguous pair of links as applied to the pivot connecting 
those links ; and, obviously, the greater the number of links assumed, 

183 



1S4 TANK CONSTRUCTION 

the more nearly will the conditions approximate to those for a 
perfectly flexible trough. 

With the dimensions indicated in Fig. 108, the length of the 
trough sheeting between the supports will be about 21 ft., and since 
both the trough and its loading may be regarded as symmetrical 
about the vertical centre line, we need only consider one-half of 
the trough. The length of skin for this being about I0'5 ft., we may 
(for the purposes of illustration) take the assumed links as about 
2 ft. in length between pivot centres. The imaginary links are 
indicated in Fig. 108, and the depth of each pivot centre below 
the brim of the tank is figured. Taking i ft. run of the tank as a 
basis, the liquid pressures applied at the pivots ma\^ be calculated. 
Thus, if the depth of some particular pivot be D ft., the intensity 
of pressure at that level will be W D lb. per sq. ft., where W is the 
weight of the contained liquid in lb. per cub. ft. With a fair number 
of assumed links, there will be but little error in regarding this 
intensity of pressure as constant between the middle points of each 
pair of adjacent links; and hence, the total liquid pressure at each 
pivot centre may be taken (in this case) as W x D x 2 ft. = 2 W D 
lb. per foot run of the tank. These pressures are indicated, acting 
in lines normal to the curve, in Fig. 108, and are lettered A B, B C, 
. . . F G, respectively. Setting out these forces to scale, the force 
polygon may be drawn as shown ; and if each intersection be joined 
with the point h, the forces which must act at the pivots in order 
to maintain equilibrium may be determined. 

To locate the point h we may argue that, since both the trough 
and its loading are symmetrical about the vertical centre line, the 
tensions F H and G H must be equal in magnitude and similarly 
inclined to the horizontal. Hence, if the force-line f g he bisected 
in 0, and a line (shown dotted in the diagram) drawn through 
perpendicular to f g, the point h must lie in that line. Again, since 
the point in which the trough sheeting meets the lower flange of the 
vertical wall-girder is assumed to be pivoted, the uppermost link 
will swing outwards under the action of the liquid pressures. Sup- 
posing h to be vertically below b, a trial link-line may be drawn ; 
and this was done in making the sketch for the illustration. This 
trial link-line (similar to the dotted link-line A H, B H, . . . F H 
.shown) was, however, found to be shorter than the added lengths 



TROUGH-BOTTOMED RECTANGULAR TANKS 



185 




00 

o 




i-i 




i86 



TANK CONSTRUCTION 



of the unloaded links ; and since this obviously could not be in 
agreement with the facts, another position for the point h was 
obtained — sHghtly to the left of the first trial position. This gave 
the dotted link-line shown, the total length of which is sensibly 
equal to that of the unloaded links. 

The point h could have been located by considering the liquid 
pressures upon a vertical plane containing the longitudinal axis 
of the tank, and thus determining the horizontal resistances, neces- 
sary for equilibrium, at the top and bottom of the trough. It does 

not follow, however, that such 
a location for h would satisfy 
the practical conditions any 
better than did the trial loca- 
tion described ; for its deter- 
mination would take no account 
of change in the shape of the 
trough under loading, and such 
changes must inevitably occur 
if the trough be flexible. 

The reader is advised to 
construct for himself several 
diagrams such as that shown in 
Fig. io8, taking different pro- 
portions for the tank and 
trough, as well as different 
shapes (not forgetting the very 
convenient semi - cylindrical 
form) for the trough, and examining for each the effects of variations 
in the surface level of the contained liquid. Some of these effects 
are described in pp. 57-60, Chapter IL 

It will be obvious that a truly flexible trough would change 
its shape very considerabty with alterations in the surface level; 
and it will also be obvious that circumferential seams — ^which are 
almost unavoidable with this form of construction — ^would not 
remain tight against leakage for long under such changes of shape, 
no matter how securely they might be made, nor how tightly caulked, 
in the first instance. Moreover, consideration of the tensions in 
the links, as indicated by the diagram, will show that no practicable 




Fig. 109. 



TROUGH-BOTTOMED RECTANGULAR TANKS 



187 



thickness for the trough sheeting could give sufficient strength and 
stiffness to maintain the shape of the trough against the loading ; 
while any increase in the thickness of the trough sheeting for this 
purpose would reduce the advantages offered by such a form of 
construction. 

The trough could, of course, be stiffened against deformation, 
either by means of curved ribs and bracing, as indicated in Fig. 
109; or by rib plates held in position by horizontal transverse 
pieces, capable of acting as ties or struts according to the require- 
ments of the loading, as shown in Fig. no. Of these two methods, 
the latter is, perhaps, to be preferred for most cases, as being the 
more effective in preventing deformation. Both methods are, 
however, somewhat costly ; and 
the advantages apparently ob- 
tainable from the use of a 
trough bottom (as against the 
ordinary flat bottom with its 
supporting floor construction) 
may be nullified if an elaborate 
system of stiffening and bracing 
be required. It must not be 
forgotten that the curving 
of the trough plating, besides 
being in itself somewhat expen- 
sive, adds appreciably to the 
costs of manufacture, transport, and erection ; and a saving in mere 
weight may be a totally false basis for comparison as regards cost. 

The form of the structure, as indicated in Fig. 107, is, however, 
unquestionably attractive for many reasons, and in the following 
pages we shall proceed to a further examination of the question, with 
a view to ascertaining whether some of the difficulties may be over- 
come by simple and practicable means, without unduly sacrificing 
the real and important advantages. 

Much valuable information may be obtained, with very little 
trouble and at a cost of only a few pence, by arranging a simple model 
of the structure. The trough may be conveniently made from a 
strip of tracing cloth slung from two stiff laths, and fine sand may 
be used to represent the contained liquid. The trough may be 




Fig. iio. 



l88 TANK CONSTRUCTION 

suspended between two vertical sheets to form the end bulkheads, 
one sheet being of glass or other transparent material, with hori- 
zontal and vertical lines scribed upon it at convenient intervals, 
so that distortions of the trough under loading may be readily 
observed and measured. 

Since the sand will have an angle of repose, the conditions will 
not be exactly like those for a liquid ; but then, as is well known, it is 
almost impossible to reproduce accurately in a model of any kind all 
the conditions of an actual structure. However, the information 
obtainable by such means is undeniably valuable, provided it be 
properly interpreted. 

\Mth a little more trouble and elaboration of the apparatus, 
more precise information may be obtained, but it is sufficient to 
give here the rough idea alone. 

By making the trough of sufficient length, the effects of bracing 
and rib-plates may be observed. It will be found convenient to 
make the ribs and rib-plates of thin wood, and to fit them outside 
the trough. A trough composed of two strips of cloth, connected 
by a plain lap seam (without an\' adhesive) '' riveted " with small 
paper fasteners, will soon show the effects likely to occur in the 
circumferential seams of a flexible trough. 

The suggested apparatus is indicated in Fig. iii. 

50. Construction of Trough Bottoms. — It will be obvious that if 
rib-plates or stiffeners be introduced to prevent distortion of the 
curved trough, the sheeting may be assumed to act as a series of 
beams between the supports. There is no particular diffiiculty in 
designing for such assumptions, of course, but much of the advantage 
offered by the trough form of construction ma}^ be lost, while there 
will be the additional cost for bending the sheeting and supports. 

There is a promising field for research in this matter ; for it is 
quite possible that, by locating the levels at which there is likely 
to be but little bending action in the trough, and arranging the trough 
sheeting in horizontal strakes with the longitudinal seams at these 
levels, the sheeting between the seams might not be seriousl}- harmed 
through the changes of shape — particularly if the surface level of 
the contained liquid be not subject to wide and rapid variations. 

Again, it is possible that, with the sheeting arranged in strips 
of (say) 5 ft. width, extending from the tank-wall girders on each 



TROUGH-BOTTOMED RECTANGULAR TANKS 



189 



^^ 1^;^;^;^;^^^^^ ^ ^\\\\\S\\\\\\sss\\s\\s\\s\s\ \v\^^^^^ 



^' I ^ 



^^ 



> 
if) 



\ \ 



(D^d) (|^-^--^-0— $- 







z 
o 

1- 
o 

ui 

< 

z 

Q 

D 

z 
o 



I— 1 



z 
o 

Ui 

V) 

vn 
o 
u 



190 TANK CONSTRUCTION 

side to the invert of the trough, it might be found sufficient to pro- 
vide adequate rib-plates (after the manner of Fig. no) at each 
circumferential seam, with a stout rib (say of bulb angle section) 
along the longitudinal seam at the invert, between the rib-plates. 
Indeed, it is possible that if the trough be carefully shaped to suit 
the loading, so that bending actions would be small at full load, 
the plates might be capable of dealing with lesser loading without 
stiff eners or framing of any kind. 

Experiments are necessary, on a reasonable scale, before any 
definite course for design could properly and profitably be laid 
down. It is useless to start theorising or calculating until more or 
less precise information has been obtained as to the manner in 
which the sheeting wiU act under variations of loading ; and it is 
obvious that there are several factors — as, for example, the effects 
of the vertical bulkheads at the ends upon the curved trough 
sheeting — ^which may exercise a powerful (and, perhaps, even a 
determining) influence upon the resultant action under different 
sets of conditions. 

From a consideration of the stresses as estimated in the diagram 
of Fig. 108, it seems likely that such research, if conducted upon 
right and broad-minded lines, might yield highly profitable results. 

There would, however, appear to be a method available by which 
the principal advantages of the trough bottom might be secured 
without much uncertainty as to the manner in which the trough 
sheeting will act. The author has no knowledge of the method 
having been tried in an actual tank, but believes that it might give 
efficient and economical construction in favourable circumstances, 
and therefore offers the suggestions for consideration. 

Primarily, this method consists of the use of flat plates for the 
main portions of the trough, supported and stayed against the 
pressures of the contained liquid, and arranged to give a section 
approximating more or less to the semi-elliptical shape which would 
provide the required storage capacity. The invert of the trough 
(which should possess ample stiffness) may be formed of a curved 
plate, bent to some convenient radius, the width being variable to 
suit the side sheeting of the trough. 

To show the application of the method, let us consider the section 
indicated in Fig. 108, and treat it on this basis. 



TROUGH-BOTTOMED RECTANGULAR TANKS 



191 



The cross-section might be as shown in Fig. 112, which will be 
found to give a capacity practically equal to that of Fig. 108. 
Using fiat plates about 5 ft. in width, laid in horizontal strakes, 
there will be longitudinal seams at A and B. These may be single- 
riveted lap joints for all ordinary cases. Unless the tank be more 
than (say) 30 ft. in length, each strake may be in one piece. If the 
length be so great as to render the use of single-piece strakes either 



15-^' 




Fig. 112. 

impracticable or inconvenient, circumferential seams will be neces- 
sary; and these may occur at stiff eners, the strakes ''breaking 
joint " as usual. 

Since the strakes will have different inclinations, it will be neces- 
sary to flange the plates for the longitudinal seams ; but the flanging 
may be confined to one plate at each seam, as indicated in Fig. 112. 
By arranging the lowermost strake so that it shall be tangential to 
the curved invert plate, and leaving flat strips along the edges of 
the latter, flanging for the invert seams may be rendered unnecessary. 

The supports or stiff eners for the sheeting may be of angle-bars, 



192 



TANK CONSTRUCTION 



with stays (also of angle-bars) cleated to them, as indicated in Fig. 
113. B}' bending the supports as shown, packing strips or other 
adjustment to allow for the lap joints in the sheeting will become 
unnecessar}'. The small pocket spaces marked P ma}- be plugged, 
or (preferably) filled with carefully fitted taper packing pieces. If 
the supports be placed outside the trough, they may be riveted to 




-♦NVLRT PLATE 



Fig. 113. 



the sheeting by means of f in. -diameter rivets, with a pitch equal 
to about sixteen times the thickness of the sheeting ; if they be 
placed inside the trough, the riveting will need to be much stronger 
and closer, to transmit the liquid pressures to the supports and to 
maintain tightness against leakage. 

It will be found that sheeting of sufficient thickness to transmit 
the liquid pressures to its supports by beam action (if the supports 



TROUGH-BOTTOMED RECTANGULAR TANKS 



193 



be spaced at reasonable distances apart) will provide ample strength 
to support the weight of the entire trough and its contents by sus- 
pension ; and that the lap seams, with ordinary riveting for tightness 
against leakage, will be subjected to very light shearing stresses. 
Since the tension in the sheeting due to the suspension of the trough 
and contained liquid will be at right angles to the stresses due to 




Fig. 114. 

the beam action, the separate stresses need not be added together 
in estimating the working stresses. 

This method should prove simple and cheap in erection; for 
the vertical tank-wall girders could be manufactured complete, in 
convenient lengths, before delivery to the site. They could be 
Hfted into position and secured ; and the trough framing, fitted and 
fixed in place, would provide practically all the support necessary 
for staging to erect and rivet the trough sheeting. 

Obviously, the thickness of the trough sheeting may be varied 



194 



TANK CONSTRUCTION 



from strake to strake if desired ; and economies could, doubtless, 
'be effected in some cases by this means. 

There would seem to be no need for consideration of the design 
and calculations in detail here, for all the loading and stresses may 
be estimated readily by straightforw^ard methods of reasoning on 
the lines previously indicated. As already stated, the invert plate 
should be fairly stiff (in all probability at least one service pipe will 
be suspended from it) ; and the horizontal stays to the supports 

should be capable of acting 
i|i^ ill ill "T "! as struts to resist such thrusts 

as are likely to be applied to 
them. 

As an alternative course, 
the whole of the trough sheet- 
ing (excepting the invert) 
might be fiat, as indicated in 
Fig. 114, the invert being 
formed either of a curved plate 
(as shown in the sketch), a fiat 
plate flanged along both edges, 
or a steel trough section, such 
as is sometimes used for the 
decks of bridges and the floors 
over subways. The relative 
advantages and disadvantages 
of such a method, as compared 
with that of Fig. 112, will be 
obvious. 

Other modifications will doubtless suggest themselves, and 
some may be convenient in particular circumstances. Generally, 
however, it should be observed that as the trough sheeting is made 
flatter, the effect will be either (with the sides sloping inwards) to 
increase the depth of the trough if the capacity is not to be reduced ; 
or (with the sides nearly vertical) to approach the conditions of the 
ordinary flat-bottomed tank, necessitating a more or less extensive 
and costly system of framing to support the sheeting. 

51. Bulkheads. — ^At the ends of the tank there must be con- 
taining walls, both to the trough and the tank proper. These end 




Fig. 115. 



TROUGH-BOTTOMED RECTANGULAR TANKS 



195 



walls are best made in the form of vertical bulkheads, after some 
such method as that indicated diagrammatically in Fig. 115. The 
vertical stiffeners may be of rolled-steel joist sections, or of bulb 
angles or tees, according to the circumstances of particular cases. 
A good arrangement is shown, in some detail, in Fig. 116 ; and this 
will need no further description. The alternative arrangement 
illustrated in Fig. 117 may be found convenient in some instances; 
and this also should be self-explanatory. 



i 



1 



h^: 



Bl/LKHEAO 
SHEETING 




kJ 



M 



r 



STIFF ENER 




Fig, 116. 



Fig. 1 17. 



With very large troughs it may be necessary or desirable to 
insert an additional main horizontal rail to support the vertical 
stiffeners, as indicated in Fig. 118. This additional rail may press 
horizontally against the end stanchions, and the outward thrusts 
should be transmitted to the tank-wall girders by means of an 
inclined tie in the end panels at each side of the tank, to prevent 
lateral loading of the stanchions. 

With fairly large troughs it may be well to provide double angles 



196 



TANK CONSTRUCTION 



for the connection of the bulkhead to the trough sheeting, with 
the bulkhead sheeting carried through to the rim of the outer angle, 

as shown in Fig. 119. If the 
vertical bulkhead stiffeners be 
placed on the inside of the 
sheeting, as in Fig. 117, the 
connections are rendered more 
difficult, and may need special 
treatment ^to ensure satisfac- 
tory results. 

For troughs of medium or 
small dimensions, the single 
angle support, placed on the 
outside of the trough sheeting, 
as shown in Figs. 115 and 
116, should provide sufficient 
anchorage for the lower ends 
of the vertical bulkhead 
stiffeners; though, in some 
cases, it may be well to provide 
additional cleats on the inside 
of the trough, as indicated at {a) in Fig. 116. 

Obviously, the angle supports at the ends of the trough must be 




Fig. II 



BULKHEAD SHEETtNG 



STIFLE NER 




vJr 



Fig. 119. 

of special form, fitting around the invert plate as well as the trough 
sheeting. These angles should be of stout section, so that they 
may not bend sufficiently to permit serious opening of the seams. 



TROUGH-BOTTOMED RECTANGULAR TANKS 



197 



The riveting in these connections, both for the bulkheads and for 
the trough sheeting, should be of close pitch and generous diameter 

throughout. 

The vertical bulkhead stiffeners may be treated as propped canti- 
levers and it will be clear that the arrangement of Fig. 116 possesses 
a real' advantage (as compared with that of Fig. 117) in that the 
sheeting is pressed outwards against the supports, while these latter, 
in turn are pressed outwards against the horizontal mam rails. 

S2.— Suspension of Troughs.— The practical construction of the 
trough-bottomed rectangular tank presents a few problems which 
are worthy of consideration. 

First of all comes the question 
of general arrangement for economy 
and convenience in manufacture and 
erection, and for conditions hkely 
to prove favourable in working and 
maintenance. 

Obviously, if the tank walls were 
placed in hne with the axes of the 
stanchions, the latter would project 
into the tank as indicated in Fig. 
120. This would cause difhculty in 
rendering the trough tight against 
leakage, for the trough sheeting 
would require to be boxed around 
the stanchions; and while some 
effective method of boxing could ^^^- ^^''' 
doubtless be devised, the work involved would be both troublesome 
and costly. Moreover, deep and awkwardly shaped pocket spaces 
would almost inevitably be left, in which, being practically inacces- 
sible for either inspection or treatment, corrosive actions might 
go on unchecked until serious damage to the structure resulted. 

To bring the stanchions closer together (transversely to the 
tank) would have the effect of throwing the tank walls towards the 
outer faces of the stanchions ; and this would tend to aggravate the 
difficulty. Hence we are led to the remaining alternative of spread- 
ing the stanchions— by which means, clearly, the difficulty may be 
overcome. 





Fig. 121. 



igS 



TANK CONSTRUCTION 



The tank walls might be carried along the inner faces of the 
stanchions, as indicated in Fig. 121; and, provided that proper 
care be exercised in arranging the details, this method will probably 
be found more convenient and practicable than any other. An 
improvement may be effected by spreading the stanchions still 
further, sufficiently to permit the vertical limbs of the outer flange 

^ angles on the wall girders to 

■^B run through, a packing strip 

-^ being inserted between the 

stanchion flange and the wall 

sheeting (or webplate), as 

shown in Figs. 122 and 123. 

The weight of the entire 
tank and its contents must be 
transmitted to the stanchions 
through the rivets which 
secure the wall sheeting to 
the stanchion flanges, and 
these rivets should therefore 
be designed on a generous 
basis. Careful attention should 
be given also to the prepara- 
tion of the holes, as well as to 
the actual driving and closing 
of the rivets, to ensure the 
best working conditions. 

Eccentric loading of the 
stanchions will be inevitable, 
but the transverse bracing 
necessary to resist the out- 
ward pressures of the con- 
tained liquid may be arranged and designed to assist the stanchions ; 
and if proper and effective use be made of this framing, and 
adequate anchorage provided at their bases, the stanchions should 
not require to be either massive or costl}'. 

The tank walls may be designed primarily as ordinarv plate 
girders for supporting the weight of the tank and trough, with their 
contents, longitudinally between the stanchions. For the upper 




Fig. 122. 



TROUGH-BOTTOMED RECTANGULAR TANKS 



199 



flange, the usual methods may be employed; but at the lower 
flange a sHght complication is introduced by the necessity for means 
whereby the trough may be secured to the girder, both as regards 
suspension and for tightness against leakage. Obviously, under the 
circumstances, there are two alternative courses open. Either the 
webplate may project through the flange, as indicated in Fig. 122, 
leaving the trough sheeting to be attached to the projection by 
means of a simple lap joint ; or the webplate may stop, as usual, 
and the trough be secured to the girder by means of double angle 
bars beneath the flange plate, as shown in Fig. 123. Of these two 
methods, the latter is preferable as giving more effective construction 
in every way, while its cost should 
not exceed that of the former. 

Since the webplate will be 
subjected to considerable shearing 
stresses, it must be adequately 
stiffened against buckling ; but 
the stiffeners between the stan- 
chions may be arranged and pro- 
portioned to transmit the outward 
pressures of the contained liquid 
to the upper and lower flanges of 
the girder, these being designed to 
act as curbs between the lateral 
supports, bracings, or ties. 




Fig. 123. 



With such tanks as are likely to be suitable for this method of 
construction a roof will nearly always be necessary, and the fram- 
ings to support the roof may be adapted to act as lateral ties to the . 
side walls. Whatever transverse loading and bending moments 
be allowed to act upon the flanges between the ties must, of course, 
be provided for in designing ; and this provision is more easily and 
satisfactorily made with the section of Fig. 123 than with that of 
Fig. 122. 

For convenience in erection, with the flange arrangement of 
Fig. 123, the wall girder may be riveted (in the yard, before despatch 
to the site) as shown at (a) in Fig. 124, with a few bolts securing the 
inner angle and flange plate sufficiently to prevent damage in transit. 
The remaining angle may be either sent loose, or (preferably) bolted 



200 



TANK CONSTRUCTION 



to the trough— as shown at {b) in Fig. 124— for deUvery. When the 
girder is in position, the pieces may be assembled as in Fig. 123, 
and the two rows of rivets P and Q driven without much difficulty. 
In the longitudinal stretches between the stanchions, transverse 
ties to the side walls will be sufficient, since the only loading to be 
resisted is that due to the outward 
pressures of the hquid — though 
framing or trussing of some kind 
may be necessary to prevent undesir- 
able sagging of the ties where these 
are of such length that they would 
be inconveniently large or heavy if 
provided with sufficient stiffness in 
themselves. 





'■-■M^M^ 



ALL MAIN MEMBERS OF 
BRACING ,R.S CHANNELS 




Fig. 125. 



At each pair of stanchions^ (transversely to the tank), bracing 
will be necessary to assist the stanchions in taking up their loading. 
This bracing may be arranged as indicated in Fig. 125, the number 
of panels being, of course, increased where the ratio B : D is more 
than can be properly dealt with in two panels. For obvious reasons, 



TROUGH-BOTTOMED RECTANGULAR TANKS 201 

the panels of the bracing should be as nearly square as may be 
practicable. 

When designing the bracings, proper consideration should be 
given to all the straining actions to which they will or may be sub- 
jected, both as a whole and in their individual members. The 
upper boom will be placed in tension by the outward pressures of 
the liquid upon the tank walls, and in compression owing to the 
eccentric loading of the stanchions — ^with the arrangement similar 
to that indicated in Fig. 121. It is highly probable, therefore, 
that this member will be called upon to act as a strut under 
some conditions of working, and should be designed accordingly. 
The length as regards flexure in the vertical plane may be taken 
as the panel length, provided that the panel points be either 
themselves properly triangulated, as in Fig. 125, or adequately 
connected with triangulated points. As regards flexure in the hori- 
zontal plane, the length must be taken as the full width of the tank 
unless node points are formed by the roof framing or auxiliary 
bracing. For tanks not extraordinarily large, the typical details 
shown in Fig. 125 may be found useful ; and for other cases it is 
probable that some simple modification of these details will meet 
the requirements satisfactorily. The lower boom will be placed in 
tension by the liquid pressures and also by the tendency to flexure 
of the stanchions in taking up their loading. Hence — ^unless the 
structure be subjected to some horizontal transverse loading (such 
as a severe wind pressure) sufficient to bring about a reversal of 
stress in these members — it is probable that the lower booms of 
the bracings will be required to act only as ties, and the suspensions 
indicated in Fig. 125 should be sufficient to prevent excessive sagging. 
The channel section is convenient for these members because it 
provides a simple and ready means for securing the ties to the 
flange plates of the wall girders ; but where this is not really 
necessary, the ties may be of some other suitable section — such as 
two flat bars tacked together at intervals with bolts and distance- 
pieces. 

At the end bulkheads, the horizontal main rails for resisting 
the liquid pressures may be made, by suitable arrangement, to 
serve also as the transverse bracings for the stanchions. Horizontal 
comer ties also may be used, where necessary or desirable, in the 



202 



TANK CONSTRUCTION 



manner described and illustrated in pages 160-163, relating to 
ordinary rectangular tanks. 

In addition to the necessity for ensuring tightness against leakage 
at the connections of the end bulkheads with the tank walls and 
trough sheeting, the weight must be properly delivered to the end 
stanchions; and this calls for a little consideration. 

A method which would probably meet the requirements satis- 
factorily in most cases is shown in Fig. 126, the sheeting of the tank 
and trough being continued past the end stanchions sufficiently to 
accommodate the circumferential angles which are to form the 
bulkhead connections. With this arrangement, if it be desired 
that the horizontal main rails of the bulkhead framing shall serve 
also as bracing for the stanchions, these members should be placed 



BULKHEAD 5HEETING 





STANCHION 



Fig. 126. 



Fig. 127. 



inside the tank, and in line with the end stanchions. If separate 
framing is to be used to form the bracing, the horizontal main rails 
may be placed outside the vertical supports, as indicated in 
Fig. 117, their loading being transmitted to the tank walls by means 
of suitable brackets. 

To prevent wringing actions in the stanchions, angle stays may 
be emplo^'Cd, as indicated in Fig. 127, securing the outer hmbs of 
the stanchions to the flange plates of the tank wall girders. It is 
desirable that such stays (or other effective support) be provided 
for all the stanchions, but they are particularly necessary for the 
end stanchions at each side of the tank, where wringing actions are 
likely to be set up through the action of the bulkhead framing and 
its connections. 

The conditions as regards the stanchions will, of course, be 
much improved by the use of suitable bracing longitudinally, and 
an appreciable saving in cost may often be effected by this means 



TROUGH-BOTTOMED RECTANGULAR TANKS 20$ 

— particularly if the tank be elevated to a considerable height above 
the bases of the stanchions. 

Other methods of arrangement and construction are possible, 
and will doubtless suggest themselves. For instance, the transverse 
framing might be made to act as a girder between each pair of 
stanchions, receiving the weights from the tank wall girders and 
transmitting them to the stanchions. Care is necessan,^ in dealing 
with the intersections of these transverse girders with the tank wall 
girders, to ensure the proper transmission of the loading without 
setting up unduly high stresses in the members and their connections, 
and also to secure tightness against leakage ; but there should be 
no real difficulty in the way of obtaining an efficient and economical 
structure on such a basis. 



CHAPTER VII 

CYLINDRICAL TANKS 

53. General Arrangement of Cylindrical Tanks. — The simplest, 
as well as the most common, type of cylindrical tank is that which 
stands upon a flat base, and is used for the storage of oil, water, 
or other liquid, or to form the reservoir of a gasholder. 

WTiere used for storage, such tanks are almost invariably 
provided with a roof, whereas in the case of a gasholder tank a 
roof would be both unnecessary and impracticable. Otherwise, 
however, there is little or no essential difference between the 
conditions for the design and construction of tanks for either 
purpose. 

Tanks of this type vary from about 20 ft. to 200 ft. in diameter, 
and from 15 ft. to 40 ft. in height. For the small sizes (and 
where the use is for storage) it is open to question whether the 
cylindrical form is the most economical; but for the larger sizes 
(and for gasholder reservoirs) the cylindrical form is unquestionably 
preferable to any other, and it is probable that much larger tanks 
of this type may be expected in the future than have been 
constructed in the past. 

The general arrangement for an ordinary cylindrical tank of 
moderate dimensions is indicated in Fig. 128. The cylindrical wall 
is constructed in strakes, the circumferential seams being always 
of single-riveted lap joints. The vertical seams also are sometimes 
made of lap joints ; but it will be shown presently that economy 
is to be obtained by making these seams of double covered butt 
joints. A stout angle forms the bottom curb connecting the 
cylindrical wall with the flat floor plating; and a light angle curb 
is usually provided at the brim if there be no gallery at this level. 
Gasholder tanks are usually provided with a gallery, cantilevered 
or bracketed out from the tank, at the brim; but storage tanks 

204 



CYLINDRICAL TANKS 



205 



do not as a rule need such galleries unless the conditions of working 
are such as to prohibit the use of a roof, and at the same time to 
require frequent and methodical inspection of the contents. 

Vertical stiffeners are generally provided, their main purpose 
being to prevent buckling or crumpling of the vertical sheeting; 
but such stiffeners may in most cases be arranged to perform 
other useful tasks as well — 

such as assisting in the sup- i""^' ''n ^'""•^ 

port of the roof framing for a 
storage tank, or forming in- 
ternal guides for the lowermost 
lift in a gasholder tank. 

The floor plating, resting 
upon a flat and solid founda- 
tion of concrete with a sufh- 
cient covering of loose sand 
to prevent the weight from 
being supported on the rivet 
heads (which would leave the 
plates to act as a series of 
beams between the seams), is 
probably almost free from 
bending stresses. It is common 
practice to make these plates 
y\ in. in thickness for all sizes 
— from the smallest to the 
largest — -of tanks, and the 
results of experience would 
seem to indicate that such 
practice is satisfactory in 
ordinary circumstances of loading and use. 

54. Roofs of Cylindrical Tanks. — The roof (for storage tanks) 
is almost invariably domed, in the form of a convex zone of a. 
sphere, this form having been found effective in throwing off rain, 
as well as being suitable from other points of view. With tanks 
of small or moderate diameter, the roof sheeting may be supported 
on light trusses spanning the full diameter of the tank, and all 
intersecting at the centre. For larger tanks it is frequently found 




206 



TANK CONSTRUCTION 



preferable to provide a central post or stanchion, with light 
trusses radiating from it to the circumference, as indicated in 
Fig. 129. Purlins are necessary, also, to provide adequate support 
for the roof sheeting without requiring too many trusses — which 
latter are, of course, somewhat costly. 

With regard to the rise of the roof, there would seem to be no 
rule in general acceptance, some roofs being given a very sharp 
rise, while others appear to be almost flat. A good deal may 
depend, of course, upon the circumstances of particular cases ; on 
the one hand, sufficient rise is necessary to prevent the retention 
of rain-water and to obtain a certain degree of strength and stiffness 
(even with very thin sheeting) through the "arching" action, 
while on the other hand it is clear that rise should be minimised 
to avoid waste of material and labour in the sheeting and trusses, 




additional wind pressure, surfaces which are so steep as to be 
dangerous for those who have to walk over the roofs for the 
purpose of. operating or attending to the tanks, and other 
undesirable effects. 

For economy in preparing the roof sheeting and trusses it is 
obviously desirable that the spherical curving should be made to 
some standard radius, so that one set of forms or templets may 
serve for tanks of all diameters by working away from the summit 
in all cases. For general suitability, however, as well as for 
economy and efficiency in the trusses, it is clearly desirable that 
the rise of the roof should bear some fixed and convenient ratio 
to the diameter of the tank; and this would give a different 
spherical radius for each different tank-diameter. It is difficult to 
reconcile these two opposing considerations, and doubtless this 
difficulty is responsible for the lack of uniformity to be observed 
in existing tanks. 



CYLINDRICAL TANKS 



207 




The adoption of a standard radius for the spherical roofing 
would result in either almost flat roofs with very shallow truss- 
ribs for tanks of small diameter, or unduly high-pitched roofs with 
excessively deep trusses for large tanks. In either case the con- 
sequence would be a need for special treatment, the cost of which 
would probably outweigh the saving obtained from standardising 
the radius of curvature. 

With tanks of moderately large diameter the rise is often made 
about one-tenth of the tank-diameter, and this proportion is not 
open to any particular criticism or objection. The roof sheeting 
is generally very light, 14 B.W.G. being a commonly employed 
thickness. As a rule, the plates are not bent to their final curvature 
before despatch to the site ; but they are, of course, shaped 
according to their position by tapering their side edges to radiate 
from the summit of the 
roof. At the centre, a flat 
circular cap-plate is used. 
The seams are usually 
single-riveted lap joints, 
with the lightest riveting Fig. 130. 

which can be made to serve the purpose. 

Seeing that a considerable amount of work and handling must 
be put upon these roof sheets, and in view of the fact that the 
•cost of riveting is more nearly proportional to the number of rivets 
used than to their diameter, the author is by no means convinced 
that the great anxiety (which is evident on the part of tank 
designers) to obtain mere lightness at all costs is really productive 
of economy. On the basis of an all-round price per ton, of course, 
it is apparent that a saving in weight means a reduction in the 
selling price; but it is at least possible that a more just and 
impartial investigation of the actual costs of production might 
prove such a basis to be misleading in many cases — particularly 
in light plate work, where the weight of the material is so small 
that its actual cost prior to manufacture is an almost negligible 
fraction of that for the finished structure. 

For small tanks the roof trusses usually consist of a curved 
rafter of light steel angle-bar and a tie-rod, without any web 
members other than a central strut or post, as shown in Fig. 130. 



208 



TANK CONSTRUCTION 



The purlins are of yet lighter angle-bars, and are put in straight 
between the trusses. Obviously, it would be a waste of time to 
attempt anything in the nature of calculation for design on the 
basis of loading and stresses for such construction, and it may 
well be thought that such methods should be considered too 
trumpery for use by competent and responsible engineers. At the 
same time, however, it is but fair to point out that failures of 
such roofs do not seem to occur — or, at least, to be recorded — and 
it is therefore difficult to substantiate any definite objection to 



ROOF 5HEtTIN& I4BWG 




ROOF FRAMir^lC 



FfOOF SHCETtNO 



PLAN 



Fig. 131. 

them. If (as the author believes) it could be shown, on the 
incontrovertible evidence of actual cost, that the adoption of 
other methods giving a more logical basis of stability would also 
reduce the costs of production, it is possible that such other 
methods might be used. Nothing short of an assured increase of 
profit is likely to bring about a change, however ; and it would be 
unreasonable to complain against this attitude in principle, though 
it is sometimes carried too far. 

A roof for a comparatively small tank — say, about 30 ft. diameter 
— typical of common practice is shown in Fig. 131, and this will 
need no further description. 



CYLINDRICAL TANKS 209 

For tanks of moderate and large diameter — say, 50 ft. and 
over — vertical stiffeners are usually employed, to prevent buckling 
of the vertical sheeting. Height is, of course, a factor in the need 
for such stiffeners, and sometimes it may be necessary to use 
them in tanks of smaller diameter if the height be great ; as a 
rule, however, the curvature of the sheeting for tanks of small 
diameter gives sufficient stiffness to prevent buckling under the 
vertical loading. The vertical loading is nearly always quite small, 
but its effect in setting up tendencies towards buckling in the 
side walls is much increased by the eccentricities caused by the 
circumferential seams (which are almost invariably lap joints), and 
the thickness of the sheeting is very small in comparison with the 
height of the tank. 

There seems to be no generally accepted rule for these vertical 
stiffeners, either as to dimensions of section or spacing ; but a 
channel section, of sufficient size to accommodate a reasonable 
amount of riveting, placed under the shoe of each roof truss, will 
be found sufficient for all ordinary cases. It would probably not 
be worth while to attempt anything in the nature of analytical 
design for such purposes. 

Where the circumstances are such that access to the roof of 
the tank is not likely to be required except on very rare occasions, 
the loading is to be solely that due to ordinary atmospheric and 
climatic conditions, and even tightness against the ingress of water 
to the interior of the tank by leakage through the roof is not 
regarded as highly undesirable, it would be waste of effort to 
suggest any methods other than the very cheapest obtainable for 
the construction of the roof. If there are to be one or more 
manholes in the roof, around which men may have to work, and 
fairly heavy concentrated loads be applied, additional strength and 
stiffness may be provided locally by means of trimming or framing ; 
and for the purposes of periodical inspection, painting, or repair, 
it may be assumed that adequate precautions will be taken by 
those responsible, to guard against possible mishap arising through 
weakness of the roof. 

Where a somewhat higher standard is desired, or where men 
may frequently be required to work on many and various parts 
of the roof, it is possible that some form other than the spherical 
p 



210 



TANK CONSTRUCTION 



might be found both suitable and advantageous. The form which 
most naturally suggests itself is that of the truncated cone (as shown 
in Fig. 132), which would seem to possess most (if not all) of the 
merits usually claimed for the spherical form, with the additional 
advantage that a standard slope of rafter may be used for tanks 
of all diameters, thus tending to uniformity in the processes of 
manufacture. A convenient rafter-slope for most cases would be 



-WEB PLATE 



4-61 




l^-S-o'-^b-o'-^i'-o'-As-o'-^'-o'-^yt-o'-^ 5-0'-^5-o'— j. 5 0'-^ 
^ . 45-0' H 

Fig. 132. 

obtained by making the ratio of rise : tank diameter equal to i : 10, 
using a standard fiat circular summit plate (giving a rivet circle 
5 ft. diameter) for all tanks. For tanks of such diameter (say, 
60 ft. and over) as to need a central stanchion to support the roof, 
the arrangement of trusses might be as indicated in Fig. 133. 

It will be seen from Fig. 131 that a large amount of cutting and 
riveting is involved with the spherical doming in common use. 




\^ S<l'-4^5k3'-^5<>'--^ 5-0'-^ S'-o'^ 5-0'^ S-o'^ 5 -O'^SO'-- 

\* 37-6' H 



-prs-o c:a. 



Fig. 133. 



Much larger plates could be used with the conical form, thus 
saving a great deal of cutting and riveting, besides giving a tighter 
and more lasting roof. 

A method of roof construction for cylindrical tanks, using the 
conical form, is shown in Fig. 134, and the author would suggest 
that the method is worthy of trial, for comparison \vith the 
methods at present employed, on the basis of economy as well as 
suitability and convenience. 

This method would permit of standardisation to a large extent, 



CYLINDRICAL TANKS 



211 



as will be seen, and should therefore be the means of saving time 
and trouble in the office, as well as in the yard and at the site. 
For tanks up to 60 ft. diameter, four full-diameter trusses might 
be used, as in Fig. 134. For all larger diameters, twelve half- 
trusses might be used, radiating from a central stanchion. 

With four trusses, the entire loading from the roof should be 
supported upon two trusses at right angles, the other two trusses 
(in halves) transmitting their loading partly to the tank walls and 
partly to the main trusses at the centre. To facilitate erection, 



ALl SCAMS IN nooF 
SMEETINS SlNSUe 
«IVtTEO LAP JOINTS 




Roof Sheeting 



Fig. 134. 

where no central stanchion is used, one main truss might be 
riveted up complete before lifting, provision being made in this 
truss for attaching the remaining trusses in halves. By means of 
a solid webplate in the central portion of the primary main truss, 
and a webplate with angle cleats on each side of the centre for 
the secondary main truss, as indicated in Fig. 135, the erection 
and fitting of the trusses could be rendered quite simple. 

The longer purlins might be in the form of light trusses, as 
shown in Fig. 136, such an arrangement providing effective lateral 
support for the trusses, and thus tending to economical design. 

By adopting a constant length (probably in the neighbourhood 



212 



TANK CONSTRUCTION 



of 5 ft.) for the panels of all trusses, working outwards from the 
edge of the summit plate, the purlins could be standardised for all 
four-truss roofs, and also for all six-truss roofs. Moreover, it is 
probable that by carefully selecting the panel length for the 
trusses, most of the purlins could be used in all roofs, whether of 
four or six trusses ; the only necessary modification being in the 
struts of the trusses, which should be splayed as at (a) or (b) in 
Fig. 136, in order to provide easy and effective attachment for the 



SuMMl"' PLATt 




SfcCTIONAL PLAN 



Fig. 135. 

purlins. With the truss arrangement of Fig. 135, no purlin will 
be necessary at the edge of the summit plate ; and at the next 
panel point the distance between the trusses will be so small that 
a plain angle of quite light section will suffice for the purlin. For 
all other panels, trussed purlins might be used, and these might 
well be of a fixed depth — say, about 2 ft. — for all spans. At the 
panel points nearest the shoes, the trusses will probably not be of 
sufficient depth to take a 2 ft. purlin, but a slight modification 
will overcome this difficulty. The trusses do not need lateral 



CYLINDRICAL TANKS 



213 



support so close to the shoes, and hence the purhns may have the 
end lengths of their lower chords inclined as at (a) in Fig. 137 — 
indeed, some such form may be preferred for all the trussed 




TWJ55 RAFTER 



»00 •CO' or 



\_ Plane of 

~ I~ TRUSS 



\f 



1 



MOBiZOMTAL SECTIONS 

ROOF TRij^SFS SHOWING, 
&PL<,Y"-<& POt; COf^NEC- 
riQNS Of c>>jgi.lN5 



T 

("^ FOff ROOF 
OF TwtLVt 
MALf TRUSetS 





f 




1 

; 




1 ®'e1 


ej 


^ 


s:^H 




<^ 


y^ 


^i 


■4 




WEB PLATE 




i 
It" 




1 :® e 


^\ 


TIE OrTf?u&S o- 


\ 



CONNECTION or PURLINS 
To TRUSSES 



Fig. 136. 



purlins, lateral support for the lower chords of the trusses being 
obtained (where necessary or desirable) by means of a light tie, 
as shown at (^) in Fig. 137. 

It will be found most con- 
venient, from all points of view, 
to suspend the purlins with 
their webs vertical ; and hence, 
for the arrangement here sug- 
gested, the struts of the roof 
trusses should be vertical also. 

The lengths of the purlins 
for standardisation may be 
easily calculated, and this point 
should not need any detailed 
consideration here. Their design (l^) 

for strength and stiffness also, Fig. 137. 

with a view to standardisation, should present no great difficulty. 

Since the purlins are to be straight and the roof sheeting 
conical, provision is necessary to ensure that the plates shall bear 
evenly upon the purlins for support. Such provision might we^^ 




214 



TANK CONSTRUCTION 



be obtained by means of hardwood packings fastened to the 
purhns by screws. The seams in the roof sheeting could either 
be arranged so that no rivets occur immediately over purlins, or 
rivets over purlins could be countersunk on the underside. The 
hardwood packings might be prepared, in strips of suitable lengths 
and widths, and screwed to the purlins before erection, all 
necessary dimensions and particulars for their preparation being 
obtainable by simple calculation. It might, however, be found 
more convenient to prepare them in the form of wedge-strips, 
which could be tapped into place after the sheeting has been laid 
in position, thus securing at once more uniform support for the 
sheeting and more uniform loading for the purlins. Thicker pack- 
ings will be necessary for the outer sheets (by reason of the lap 




Fig. 138. 



seams) than for the inner sheets, and this adjustment may be 
made either by means of additional strips where necessary, or 
full-thickness packings — the latter being preferable. This point 
tends to favour the wedge-strip packings tapped into position 
between the purlins and sheeting. 

The roof sheeting might be cut from plates of suitable width 
as indicated in Fig. 138, thus largely reducing the amount of 
cutting and waste, as well as effecting a considerable saving in 
riveting, in comparison with the spherical doming of Fig. 131. 
The most convenient width of plate may be readily determined 
for any diameter of tank by simple calculation, and all the 
roof plates could then be prepared so as to be interchangeable. 
Thus, for a tank 40 ft. diameter, with the pitch-circle in the 
summit plate 5 ft. diameter, the roof sheeting to cover the 
top curb (of 3 in. X 3 in. angle), the calculation would be as 
follows — 



CYLINDRICAL TANKS 21$ 

Extreme outer circumference 

= 7r X 40-5 ft. = 3*1416 X 486 in. 
= 1527 in. 

Taking a width of 4 ft. at the circumference of the tank as a 
first approximation — 

^~~^. — ■ = 31-8 plates. 
48 m. ^ ^ 

Now, there are to be eight truss-rafters ; and although the roof 
sheeting is to bear upon the rafters, there is no need to rivet them 
together. Hence, it will be convenient to take the nearest even 
multiple of 8 for the number of plates — in this case, obviously, 32. 
By this means it may be ensured not only that no seam in the 
roof sheeting shall occur immediately over a truss, but also that 
each truss shall be in contact with the same kind of roof plate — 
i. e. either all inner, or all outer plates, instead of some inner 
and some outer — the advantages of such a course being apparent. 
With a larger tank, having a central stanchion and twelve half- 
trusses, the number should be an even multiple of 12. 

Adopting 32 plates for the purposes of our example, the width 

1^27 in 
at the circumference of the tank will be ~^^—^ — - = 4772 in. This 

will be the distance between the centre lines of the rivets, measured 
on the curve, and the necessary laps must be added on each 
side. 

The corresponding width at the circumferential seam connecting 
the conical sheeting with the summit plate may now be determined. 
The circumference of the pitch-circle will be tt x 60 in., and the 

distance between the straight seams - — = 5-89 in. A 

32 

common lap for such sheeting is 2 in., and this would give a plate 
width about 4772 + 5*89 + 4 = 57*6i in. It would probably be 
found cheaper to use stock plates 5 ft. in width, giving laps just 
over 3 in., but saving a good deal of cutting. 

A templet could be made, either in wood or steel, the dimensions 
being obtained by calculation from the conical form, as shown in 
Fig. 139, and the plates marked for cutting and holing. The 



2l6 



TANK CONSTRUCTION 



plates would doubtless need straightening and dressing after shear- 
ing — the rivet-holes might be punched before the shearing — and 
it would greatly facilitate the work of erection if the plates were 
shaped to the conical form instead of being merely flattened. 

This could be done without heating the plates, by hammering 
in a suitable " form," and such a form could easily be made to 
take all plates if a standard slope for the conical roof were adopted, 
distances from the summit plate being marked in the trough to 
indicate the position in which any particular sheet is to be laid 
to suit a given tank diameter. 




Fig. 139. 

It would almost certainly be found cheaper to use packings 
between the summit plate and the inner conical plates, instead 
of thinning out the corners of the outer plates to allow for the 
lap-joints; and similarly, to pack between the top curb and the 
outer conical plates at the circumference of the tank. 

For marking the plates, it is probable that the employment of 
one sheet, carefully set out as a " master," would be found prefer- 
able to the use of a wooden templet. Methods for simplifying the 
work of setting-out — such as the preparation of a set of stock 
" curves," varying in radius by 6 in. or i ft., with centre lines clearly 
marked, as indicated in Fig. 140 — will doubtless suggest themselves. 

The length of each plate might be easily calculated from a 
diagram, such as that of Fig. 141, showing the " rise and going" 
dimensions of the conical slope. For the 40 ft. tank considered 
-above — 

Length of plate 

= V(i775)' + (4-0)' = ^315-0625 + 16; 
= V33i'o625 = i8-2 ft. = 18 ft. 2| in. ; 



CYLINDRICAL TANKS 



217 




Fig. 140. 



adding 7I in. for lap at the summit plate and to allow for cutting 
to curve at the outer circumference, a suitable and convenient 
length would be 18 ft. 10 in., as shown in Fig. 138. 

The riveting for tank roofs varies considerably with different 
manufacturers. With 14 B.W.G. sheeting, J in. rivets at 2 in. 
pitch are common ; but with thicker plates, and if the roof is to be 
no more than a lid, both diameter 
and pitch may be increased with 
advantage. 

Obviously, much will depend 
upon the circumstances of each 
individual case in determining the 
necessary riveting. If the liquid 
to be stored is water, no very 
elaborate precautions against either 
the ingress of moisture or evapora- 
tion of the contents may be necessary. On the other hand, if the 
tank is to contain some highly volatile liquid, or some substance 
which would be damaged by the leakage of rain or snow, care 
must be taken to render the roof secure against such faults. These 
are special matters, however, and therefore need not be discussed at 
length here. 

55. Floors of Cylindrical Tanks. — As already stated, the floor 

plates in tanks which stand 
-Jl-y upon a fiat bed of concrete 
'' - are usually J in. or -f^ in. in 
thickness for all diameters 
of tank. The seams are of 
single-riveted lap joints, 
with 2 in. or 2J in. laps ; 
and the corner of the 
middle plate is thinned out (as described and illustrated in Chapter 
III, Fig. 31) to provide for the junction of three plates. For the 
rivets, | in. diameter at 2 in. pitch is fairly representative of 
common practice, though departures may be found in some cases. 

Clearly, if the plates were uniformly supported throughout the 
floor, the main function of the riveting would be to ensure tightness 
against leakage under the full liquid head. The only straining 




Fig. 141. 



2l8 



TANK CONSTRUCTION 



actions to which the rivets would be subjected in such circum- 
stances would be those due to such causes as initial and secondary 
stresses, and the effects of temperature changes. As will be shown 
presently, however, uniform support for the floor is not likely to 
be realised in commercial tanks; and hence the rivets are in all 
probability subjected to more or less severe straining actions 
through the bending of the plates. But if reasonable care be 
taken in erecting the tank, the plates cannot bend much without 
finding improved support ; and this factor, combined with the 
necessity for closely pitched rivets to ensure tightness, renders 



BlACKED-tN CORNERS 
TO B£ THINNED 




Fig. 142. 

treatment of the seams for strength unnecessary in all but 
exceptional circumstances. 

The plates, obviously, should be as large as possible consistent 
with economy and convenience in manufacture, handling, and 
transport, for by this means riveting may be minimised. Dimensions 
in common use are 24 ft. by 5 ft., these having been found most 
suitable from all points of view. The layout should be such as 
will give all (or as nearly as possible all) the rectangular plates of 
uniform shape and size, while reducing to a minimum the unavoid- 
able cutting, waste, and riveting, for the shaped plates around the 
circumference. 

A plan for a small floor is indicated in Fig. 128, and one for a 
medium-sized floor — 100 ft. in diameter — in Fig. 142. 



CYLINDRICAL TANKS 



219 



In laying out the floor-plating, the number of rows may be 
odd (as in Fig. 142) or even (as in Fig. 143), according to the 
ratio borne by the diameter of the tank to the effective width — 
i. e. the distance between the centre lines of the long seams — of 
the floor-plates. 

Taking the tank as 100 ft. diameter over the bottom curb, for 
instance, with the centre lines of the seams 4 ft. 9! in. apart, the 
number of plates would be 100 -f- 4Vi = 2400 ^ 115 = 20*82. A 
suitable arrangement, then, might be obtained with 19 full-width 
rows (giving a total width of 19 x 4 ft. 9 J in. = 91 ft. oj in.), 



BLACKEO-tN CORNERS 
TO BE THINNED 




Fig. 143. 

leaving the two shaped plates to make up the remaining 8 ft. iij in. 
— or, rather, say, 8 ft. 11 in., since the plate should not extend to 
the face of the curb — between them. 

With a tank 95 ft. diameter, the arrangement might be as 
shown in Fig. 143, using 18 full-width rows; or, alternatively, 19 
full-width rows might be used, with smaller (extreme) shaped 
plates, as in Fig. 144. The total length of seams with the former 
arrangement is approximately 1632 ft. (1364 ft. in the long seams, 
and 268 ft. in the 5 ft. seams) ; while the latter plan has about 
1729 ft. run of seams (1468 ft. in the long seams, and 260 ft. in the 
5 ft. seams). Hence, it would appear that a saving of nearly 6 per 
cent, in the riveting may be obtained by adopting the arrangement 
of Fig. 143, instead of that shown in Fig. 144, for such a case. 



220 



TANK CONSTRUCTION 



There are, however, other factors needing consideration in 
determining the most suitable layout for a tank floor; and 
although 6 per cent, saving in the total length of seams represents 
an appreciable item in a large floor, the advantage may easily be 
lost if the layout involve a need for special care through some 
departure from the usual course of handling or erection. 

One such factor is the influence exercised, both in manufacture 
and erection, by a basic symmetry of arrangement, and uniform 
order of procedure. If some tank floors have an even and some 
an odd number of rows, confusion may arise through the former 
having a seam along a diameter of the floor, while the latter have 




Fig. 144. 

not. With a layout such as that indicated in Figs. 142 and 144,' 
a pivotal plate may be laid down at the centre of the floor, and 
the work of assembling and riveting may then proceed symmetri- 
cally along lines radiating outwards in all directions, with obvious 
advantage ; whereas with the arrangement of Fig. 143 there is no 
such symmetry. Further, in the floors of Figs. 142 and 144 the 
shaped plates around the circumference will be exactly alike in 
fours as regards shape, dimensions, and setting out for riveting; 
whereas with the arrangement of Fig. 143 these plates will be 
alike in pairs only as regards shape, dimensions, and rivet centre 
lines. 

This means a relatively large increase in trouble throughout 
the office work, manufacture, transport (including such incidentals 



CYLINDRICAL TANKS 221 

as marking, sequence of delivery, schedules, marking plans, etc.), 
and erection, the cost of which must obviously be considerable. 

It is probable that the best results from all points of view are 
likely to be secured by the adoption of a layout similar to those 
indicated in Figs. 142 and 144 for tanks of all diameters, unless 
special and exceptional circumstances render a departure necessary 
or desirable. 

The plates marked 7 and 17 in Fig. 142 would be more than 
24 ft. in (extreme) length; but in most cases it will be found 
preferable to have them thus longer than the rectangular plates — 
provided they be not so long as to involve disproportionate extra 
cost for rolling or transport — rather than to introduce additional 
transverse seams by using shorter plates. This is a point which 
arises frequently in arranging the layouts for such floors, and it 
often needs careful treatment to ensure the most satisfactory 
results. 

In Figs. 142, 143, and 144, the plate corners requiring to be 
thinned are indicated by blacked-in quadrants. As will be seen, 
the rows are laid alternately "lower" and "upper" — thus, the 
row I — 23 in Fig. 142 is a lower row throughout ; the row 2 — -22 
an upper row throughout; row 3 — 21 lower; row 4 — 20 upper; 
and so on. Within the rows themselves the plates will be alter- 
nately upper and lower if lap joints be used throughout. Hence, 
the pivotal plate at the centre of the tank will be a lower plate in 
a lower row (indicated by the mark " L L") ; while those at each 
'end of it will be upper plates in a lower row (indicated by the mark 
" U L"). In the next row (2 — 22) the order will be alternately a 
lower plate in an upper row (marked " L U"), and an upper plate 
in an upper row (marked " U U "). 

Now, it will be clear that the upper plates in a lower row (U L) 
must have their corners thinned to allow the upper-row plates to 
lie flat along those of the lower rows, while the lowermost plates (L L) 
must have their corners set downwards to accommodate the thinned 
corners above them. Similarly, the lower plates in an upper 
row (L U) must have their corners thinned, while the uppermost 
plates (U U) must have their corners set upwards to accommodate 
the thinned corners beneath them. 

It should be noticed that the object in view is to keep the 



222 TANK CONSTRUCTION 

upper surface of the lower rows, and also the lower surface of the 
upper rows, fiat throughout the floor. On this basis the thinned 
comers and the set corners may be located easily. As will appear 
from an inspection of Fig. 142, every plate comer in the floor is 
either a thinned corner or a set corner. 

Around the circumference of the floor, the plates meeting the 
curb will be alternately upper-row and lower-row plates. The 
lower surface of the curb angle should be regarded as lying at the 
same level as the upper surface of the lower-row plates which are 
to be connected with it, and the upper-row plates must have their 
curb corners thinned to make their way between the lower-row 
plates (which must have their corners set downwards) and the 
curb. 

Thinning and setting the corners of such plates are inevitably 
an expensive proceeding. A plate 24 ft. by 5 ft. is an awkward 
and troublesome thing to hold for the heating and working of its 
comers one (or even two) at a time. Corners must be heated for 
thinning; and although the set corners are commonly ignored in 
the yard (the plates being sent to the site flat, leaving the sets to 
be imposed by the riveting), it is probable that the cost of the 
job might be reduced rather than increased if these comers were 
properly set in the yard before despatching the plates to the site. 

Considerable expense is incurred also on almost every job 
through time spent on these thinned-corner junctions, both in 
coaxing the plates into position for riveting, and also afterwards 
in persuading them to abstain from leaking. 

Wedge-shaped packings (see Fig. 32) might be used instead of 
the thinned corners ; but it is open to doubt as to whether the 
cost of a floor would be reduced by such means. The packings 
themselves are somewhat costly to make, while they render the 
set corners more complicated than they are with the thinned 
corners. Moreover, wedge-shaped packings do not by any means 
simplify the work of assembling the floor-plates ; and they 
sometimes give rise to leaks which are very troublesome to cure. 

In passing, it is worthy of notice that, with the corners of the 
lowermost plates all set downwards, the plates alternately " upper " 
and " lower," and the rivet heads projecting at different levels, 
the underside of such a floor is by no means flat ; and hence, the 



CYLINDRICAL TANKS 



223 



common assumption that the floor-plates will be free from bending 
actions is not likely to be realised. Even with a fairly thick layer 
of sand spread evenly over the concrete base, the loading cannot 
be distributed with any degree of uniformity ; and bending actions 
in the plates are therefore inevitable with a layout such as those 
indicated in Figs. 142, 143, and 144. 

The author recommends, as tending towards facility and economy 
in the manufacture and erection of such floors, that the transverse 
(5 ft.) seams be of single-riveted butt joints, with inside covers, 



^.^^^-^ 




ALTERNATIVE PLAN 
FOR EXTREME 
SHAPED PLATES 



Fig. 145. 

instead of lap joints. By this means all thinning and setting of 
plate comers would be obviated, packing strips being inserted 
between the bottom curb and the lower floor-plates to fill the 
spaces caused by the use of lap joints for the long seams. A layout 
on this basis for a 100 ft. -diameter tank is shown in Fig. 145. 
The butt covers for the transverse seams would not involve any 
more material than lap joints ; and the additional cost for the 
extra holing and riveting should not represent more than a low 
percentage increase, since in the layout of Fig. 144 the total 
length of the transverse seams is but 260 ft. (for the whole floor), 
as against 1470 ft. for the long seams. Adding to this considera- 



224 



TANK CONSTRUCTION 



tion the fact that each butt cover could be riveted to one plate 
in the yard, it will be seen that the proposal should give an appre- 
ciable saving in cost, as well as a distinctly better job. Each pair 
of adjacent rows would come together without need for coaxing to 
form the long lap joints, and thus a good deal of time should be 
saved in erection. 

The butt covers (and also the packing strips at the curb) would 
need a little care in preparation to ensure their fitting the lap 
joints properly — without requiring to be chipped, and without 
leaving gaps during assembly at the site — but this need not cost 
much if taken in hand with intelligence. Using inside covers only, 
those for the upper-row plates would extend the full width of the 




r (a) 



Fig. 146. 



plates, taking two of the lap seam rivets at each end, as shown 
at [a) in Fig. 146 ; while those for the lower-row plates would fit 
between the lap joints at each end, as at (b) in Fig. 146. Alter- 
natively, the butt covers for the lower-row plates might be fitted 
on the underside, and extend the full width of the plates, becoming 
thus exactly like those for the upper-row plates. The main 
objection to this latter method is that the plates might not butt 
together truly, and leakage into the joint — if not through it — 
might be difficult to prevent in consequence. However, the inside 
cover also is open to a similar objection in that leakage at its ends 
could find an easy escape owing to the butt not being covered on 
the outside. Beyond question, the best method would be to use 
double covers for the butt joints of all lower-row plates, as shown 






CYLINDRICAL TANKS 225 

dotted at (b) in Fig. 145 ; and even with this refinement it is 
probable that the floor would be actually cheaper than with the 
plate corners thinned and set for the use of lap joints throughout. 

The packings between the curb and the lower-row plates might 
be arranged as indicated at (c) in Fig. 146, and if reasonable care 
be taken in preparing them it should be a comparatively simple 
matter to secure tightness by means of caulking. These packings 
could, doubtless, be all formed of the " waste " from the shaped 
plates around the circumference. A floor constructed on this basis 
would obviously find more uniform support under ordinary con- 
ditions than could one of the type illustrated in Figs. 142, 143, 
and 144. 

A point of practical interest and importance arises in con- 
nection with the shaped plates around the circumference of the 
floor. 

For ordering these plates from the mills, a method commonly 
employed is to set down the layout for the complete floor — or so 
much of it as is repeated — to a fairly large scale ; sometimes it is 
even laid out full size on the templet floor. The necessary length 
of each plate, to allow for shaping, is measured from the layout, 
and the plates are then ordered rectangular, with the result that 
not only is a good deal of waste material purchased, but a more 
or less considerable sum is paid for the carriage and handling 
of that waste, while the plates have still to be shaped after 
delivery. 

Now the. plates may be at least as cheaply shaped at the mills 
if the necessary particulars be supplied; and although the waste 
material must be paid for (which is but fair), transport costs will 
be reduced, while an appreciable saving both of time and trouble 
should be effected by having the plates correctly shaped, and 
marked for position in the floor, before delivery. 

The necessary particulars may be readily obtained by means 
of simple calculation; and with a little care and thought they 
may be supplied to the mills in such a manner as to ensure 
satisfactory results. 

Working on the main rivet centre lines as chords intersecting 
a diameter of the circle at right angles, the lengths of these chords 
may be calculated from the known dimensions ; for the case is then 
Q 



226 



TANK CONSTRUCTION 



similar to that illustrated in Fig. 147, where, since c^ = V (D — V), 

c = VvTd - V). 

The value of D is, of course, constant for all the chords in a given 

tank; and the appropriate value of 
V may be determined easily for each 
chord. 

Consider, for example, the plate 
marked " 8 L U " in Fig. 142 . Taking 
the tank as 100 ft. diameter over 
the bottom curb, and allowing for 
the edge of the fioor plating to be 
set in J in. behind the face of the 
curb, D for our purpose will be 99 ft. 
iij in. 

Treating the upper chord first, V 
will be {49 ft. iif in. — 7J (4 ft. 
9I in.)j = 49 ft. iif in. — 35 ft. iij in. = 14 ft. o\ in., while 
(D — V) will be 99 ft. iij in. — 14 ft. o\ in. — 85 ft. 11 in. Then — 




Fig. 147. 



c = v^h^mi=^^^^-^'^ 



\ 24 



X 



12 



337 X 2062 



24 24 

^ A/337 X 2062 ^ \/694,894 ^ 833-60 
24 24 24 

= 3473 ft. 
= 34 ft. 8f in. 

It is not much use working to greater refinement than the 
nearest eighth-of-an-inch in such matters; for not only will this 
give as good a job as is necessary for the purpose, but the use of 
sixteenths tends to confuse rather than to simplify the marking^ 
without giving any greater accuracy in shearing. The approxima- 
tion should, of course, be reserved until the end of the calculation. 

Various methods for performing the arithmetical work will 
doubtless suggest themselves, and some may be more convenient 
than others in particular cases. That shown in the above calcula- 
tion is preferred by the author for ordinary use ; it is simple, 



CYLINDRICAL TANKS 227 

and possesses other good points which will be apparent on 
consideration. 

Assuming that the rectangular plates are of such length that 
the centre lines of the short seams are 24 ft. apart, the length of 
the plate under consideration will be 34 ft. 8| in. — 24 ft. = 10 ft. 8fin. 
at its upper edge. 

For the lower chord, V will be 14 ft. oj in. + 4 ft. 9J in. 
= 18 ft. 10 in., and (D — V) will be 85 ft. 11 in. — 4 ft. g\ in. 
= 81 ft. ih in. Hence — 



c = v^sw^si^ = Vfl X ^f 



452 1947 
24 24 

_ V452 X 1947 _ -\/88o,044 _ 938-11 
~ 24 ~ 24 24 

= 39-09 ft. 

= 39 ft. ii in. 

Subtracting the length of the rectangular plate, the required 
length of the plate under consideration, at its lower edge, will be 
39 ft. ij in. — 24 ft. = 15 ft. ij in. 

In making the calculations for a floor, it is well to work on a 
definite plan and sequence, tabulating all important data as 
obtained. The work may be expedited by such means, while 
errors are less likely to occur, and checking is facilitated. 

A schedule of the shaped plates should be supplied to the 
mills, giving a dimensioned sketch for each plate with its marking. 
Thus, the sketch for the plate " 8 LU" of Fig. 142 would be as 
shown in Fig. 148, and the schedule would indicate the number 
and particulars of the plates to be cut to the given dimensions. 
For instance, with the floor of Fig. 142, there would be another 
plate, marked " 30 L U," exactly similar in all other respects to 
that shown ; and two others to the same dimensions but " opposite 
hand," one marked " 16 U U " and the other marked " 38 U U." 
It would not be necessary to mark each of these plates separately 
from the sketch ; one could be marked and sheared, and this 
would serve as a templet for the other three plates. The " opposite 



228 



TANK CONSTRUCTION 



hand" effect may be obtained by marking off these plates on the 
reverse side — and even this refinement may be dispensed with if 
there be no objection to the reversal of the effects due to shearing. 

The markings "LU" and "UU" quoted in the foregoing 
description relate, of course, to the thinned-corner plan of 
Fig. 142. With the short seams butt jointed, as in Fig. 145, the 
row-marks need only be " L" (indicating " lower row") and " U " 
(indicating " upper row") in addition to the positional numbers. 

A templet-curve, of 49 ft. iif in. radius for the case considered 
above, should be supplied with the schedule, and clear instructions 



templIet-curve. 

4-3'^' 8.LU 




10-8^ 



-\ 



J\ 



4-3!6 



.1 



\i 



15-1%'- 



LAP 



-yy 



Fig. 148. 

given for its use in marking-off. Using Fig. 148 for reference, 
these instructions might be as follows : " Set out the main rivet 
centre lines A B and C D, 4 ft. gj in. apart, truly parallel with 
each other and as nearly so with the plate edges as may be. Set 
out the transverse rivet centre line B D, truly perpendicular to 
A B and C D, and providing ij in. (if lap joints are to be used 
for the short seams) for lap. Carefully lay off the dimensions 
A B and C D shown in the sketches, and apply the templet-curve 
provided (give distinguishing number or other mark on templet- 
curve, and clearly indicate the marking edge) to obtain the curved 
line A C to which the plate is to be sheared." 

This is a typical case in which considerable economies may be 
effected through the exercise of proper care and skill in ordering 
material. 



CYLINDRICAL TANKS 229 

If the short seams are to be butt joints, as indicated in Fig. 145, 
modification in the stated lengths will be necessary, it being obviously 
desirable that the lines used for setting out shall be rivet centre 
lines rather than plate edges. Such modification is, however, too 
simple to call for detailed description here. 

The templet-curve (which should be made in duplicate, one 
being retained as proof in the event of dispute or error) should 
be carefully protected against damage in transit. It may be 
made of thin sheet steel, and if laid between two stiff boards — 
one suitably recessed to receive the templet — should come to no 
harm in ordinary circumstances. If the templet-curve be cut 
from a straight parallel strip of sheet, and the back edge left straight, 
as shown in Fig. 149, there can be no confusion or doubt as to which 
is the marking edge. 




Fig. 149. 

A stock set of templet-curves could be made, so as to be ready 
for use when required, and it is probable that no great harm would 
result from using the nearest 6-in. radius for floors of moderate 
and large diameters. 

The templet-curve may be set out by that simple method — 
which, by the way, appears to be nothing like so well known now- 
adays as it was to the wily and resourceful (if somewhat secretive) 
templet makers of a few years ago — based on the fact that the 
angle in a circular segment is constant. With the addition of a 
further device from Euclid — which device the author believes is 
by no means so well known as it deserves to be — this method may 
be made to yield thoroughly satisfactory results without the need 
for large and costly floors on which curves may be struck. 

This device consists in an application of the fact that the angle 
in a segment is equal to the alternate angle between the chord and 
the tangent to the circle at its extremity — thus, in Fig. 150, the 
angle A B C is equal to the angle D A C. This fact may be utilised 
in constructing the profile board which is to represent the angle 



230 



TANK CONSTRUCTION 



in the segment, and which (provided with a suitable scriber fixed 
at its apex, and made to swing into all positions possible for the 
segment angle by means of a nail driven at each end of the chord 
A C) will strike out the circular arc A B C to the required radius. 

Suppose the curve is 50 ft. radius, and the templet is to be 
about 8 ft. (a convenient size) in length. Then, take (Fig. 150) 
A E = E C = 5 ft.— ^. e. i ft. more than half the length of the 
templet — and set this down on a fiat board, as indicated in Fig. 151, 
clipping the templet strip in position as shown. 




Fig. 150. 



AE 



Now (Fig. 150), j~^ = cos <^, and since both A E and A O are 

known, Cos <;^ may be calculated. For the case proposed, Cos <^ = 

= o-i; whence, from the tables, <^ = 84° — 15'. Adding to 

this 90° [i. e. the angle D A O), ^ = 84° - 15' + 90° = 174° - 15' ; 
and this is the magnitude of the angle A B C in the segment. Sub- 
tracting this from 180°, the remainder is 5° — 45', and halving 
this remainder, 2° — 52' is obtained for each of the angles B A C 
and B C A. From the tables, tan 2° — 52' = 0-0501 ; and since 
A E = 60 in., B E = 60 in. x 0-0501 = 3-006 in. 

On a second piece of board, as indicated at [a) in Fig. 151, set 
out the isosceles triangle A B C to these dimensions, making this 
board about 20 ft. in length. Cut this board to the triangular 
shape set out, but leave a substantial piece on around the apex B, 
and fit a scriber or pencil through the board at B. If nails be 
driven at A and C on the first (or base) board, and the second board 



CYLINDRICAL TANKS 



231 



(cut to the triangular shape) be made to shde round so that its 
two limbs are always in contact with the nails, the scriber or pencil 
at B will sweep out the circular arc required on the steel strip for 
the templet. 

Instead of a solid board, as at (a) in Fig. 151, a light frame 
may be built up of battens to the required dimensions ; or a shorter 
chord may be taken — say, 2 ft. 6 in. instead of 5 ft. — and the curve 
drawn in two parts. 



TEMPLET -5TR1P 




5£r] 



Fig. 151. 

Another method which might be used is by the calculation of 
offsets on a chord. 

To avoid the use of a very long templet-curve, intermediate 
chords may be calculated for the plates at the ends of such rows 
as 9 — 15, and 10 — 14, in Fig. 142 ; while the extreme plates — such 
as those marked 11, 12, and 13 in Fig. 142 — may be given two or 
more intermediate chords as necessary. 

If the rivet centre-lines be laid out symmetrically about two 
mutually perpendicular diameters of the floor, the markings will 
repeat on plates similarly placed. Hence, the plates may be 
regarded as forming groups, and one plate may be marked and 



232 



TANK CONSTRUCTION 



drilled to serve as a master for all others of the same group. More- 
over, a large proportion of the marking for the main rectangular 
plates forming the body of the floor should repeat on all plates; 
so that much of the drilling may be done from a single master 
plate. 

For the shaped plates, around the circumference, the holes for 
the straight riveting should be drilled — or at least set out — from 
a rectangular master plate so far as possible, any specially spaced 
holes to fill in broken pitches near the curb riveting being left for 




TT-r + + f4- -t- + -r -r .-r 



'<;'^''ll / 1/ U-STOCK PITCH- 
/ ?^ TOiBUlT SE*iM-LAPS — 



MAKE-UP PITCHES 



^1 



MAKE-UP PITCHES - 



STOCK PITCH 



^\ >+ ->• 4--f4f-t- + -t--*--t-+-h + + -f + -(- + +-t--f-H-t-44--t-4- -tp-t- + + -I- -^-kf^ 



^\ 



TO SUIT SEAM-LAPa 



To SUIT SE.AM-LAR5 



^ 



Fig. 152. 



drilling (or punching) separately. The curb riveting should be 
set out with extreme care, and drilled with precision, on each plate 
which can be used as a master for others. A " left-hand" plate 
may be drilled from a "right-hand" master by turning back-to- 
front, provided there be no special features which would be rendered 
inaccurate by such treatment. 

A rivet should occur at each intersection of the straight and 
curved pitch-lines, as indicated in Fig. 152 ; the intermediate 
rivets being set out to suit the long seams, and at the same time 
to give as nearly uniform pitch as possible. 

By this means the setting out and drilling may be performed 



CYLINDRICAL TANKS 



233 



without requiring large floor area ; and with such accuracy as will 
ensure the plates coming together easily, and true to dimensions, 
when assembled at the site. 

The bottom curb angle should, if possible, be drilled with the 
plates to which it will be riveted, for obvious reasons ; and it should 
be curved to its proper radius before drilling. Internal covers, of 
sufficient length to prevent leakage, should be provided to all 
joints — which may be plain butts — in the curb angle. Clearly, 
the curb should be in the longest lengths 
consistent with facility and economy 
in the handling and transport. 

56. Erection of Floors on Solid 
Bases. — "Erection" is, perhaps, not a 
good word for the processes involved 
in the final preparation and fixing in 
position of the floor for a tank to stand 
directly upon a base of concrete at 
ground level ; but it is sometimes less 
dangerous to use a poor word which is 
in common acceptance than to intro- 
duce a new one. 

The riveting of the floor-plates to 
each other and to the bottom curb 
involves a practical difficulty in the 
need for sufficient clearance beneath 
the plates to permit the insertion and holding-up of the rivets — 
indeed, the rivet furnaces themselves must be accommodated 
beneath the floor if good riveting is to be obtained. 

This usually means that, with a floor of moderate or large 
diameter, the plates must be supported at some considerable height 
(not less than 4 ft.) above the concrete base until the riveting of 
the floor is complete ; and afterwards the whole floor must be 
lowered into position. 

One commonly employed method for effecting this is to form 
circular holes, about i ft. diameter, in the plates, through which 
vertical screws may project, each engaging with a bridge-piece 
spanning the hole, as indicated in Fig. 153. After the floor has 
been lowered into position upon its base, the screws and bridge- 




■ ^%.- CONCR ETE BASE Z^T^i^i^'^ 

Fig. 153. 



234 TANK CONSTRUCTION 

pieces may be removed, and the circular holes closed by means of 
cover-plates bolted to the floor-plates. 

It will be obvious that the plates are inevitably subjected to 
uneven straining actions while supported in this manner, and even 
more so during lowering. Moreover, there can be no certainty 
that the floor will find anything approaching uniform bearing 
upon the concrete base when lowered ; and while it is but fair to 
state that trouble seldom seems to arise from this cause, it is not 
possible to regard the method as satisfactory. Perhaps the most 
serious charge which lies against this method is the large amount 
of time and labour occupied in lifting and supporting the plates, 
and lowering the whole floor. The cost of this incidental work is, 
obviously, considerable. 

Sometimes, where plenty of space is available, the floor is 
riveted while supported on sleepers at the side of the concrete 
base, and rolled into position when complete. The gear necessary 
for the rolling, and the straining actions applied to the floor, render 
this method even less worthy of approbation than that described 
above ; while it is seldom that a site affords the necessary space. 

With small floors the plates may be suspended from the lifting 
tackle to be used afterwards for hoisting the wall-plates and roof ; 
but even then it is inevitable that the floor is subjected to highly 
undesirable straining actions while being lowered into position. 

The whole problem calls for consideration with a view to finding 
improved methods ; and it is to be hoped that those who are in- 
terested will soon make some real effort to obtain a practical solution. 
The author is inclined to the view that there is in this direction a 
promising opportunity for the employment of electrical or flame 
welding; and if some simple arrangement were devised, and the 
cost of the welding made reasonably comparable with that of 
ordinary riveting, the saving in time and trouble should offer a 
sufficient inducement for tank constructors to try the experiment. 
It goes without saying that there are difficulties to be overcome, 
and the plates would doubtless need special preparation; but, on 
the other hand, the cost of holing and riveting would be saved, and 
if the resulting floor were satisfactory as regards durability and 
tightness against leakage, even some additional outlay in respect 
of the actual work might be more than repaid by the saving in 



CYLINDRICAL TANKS 235 

time effected. Possibly some such arrangement as that indicated 
in Fig. 154 might form a basis for trial, the plates fitting against 
junction strips of T-section at all seams. Small folding wedges 
might be used at intervals, as shown, to act as cotters in holding 
the plates and strips firmly in position for welding. The bottom 
curb angle might then be welded to the floor-plates. 

Another method which might be tried is to rivet an angle-bar 
along each edge of every plate, as indicated in Fig. 155, the butting 
angles being easily riveted together from the floor surface when 
finally assembled in position. At the corners the angles should 
be mitred, but as the work of preparing them would be almost 
entirely repetition for all tanks, it need not be costly. Around 
the circumference of the floor the curb angle should form part of 





XJ£i^*T.T" ^-FLOOR PLATES 

■Kf':l'^y^fii$^-f^.^i^J^:^::p.',^'' section 
' concrete base 

Fig. 154. Fig. 155. 

the framing for each shaped plate. At points in which transverse 
joints meet long joints, and also around the circumference, the 
angles might not come truly together; but the openings could 
probably be filled with rust cement, or they might be welded. 

These suggestions are offered mainly with the object of stimu- 
lating interest in the problem, which is obviously worth solving. 
No matter how diflicult a problem of this kind may appear, if 
practical men can be induced to appreciate the need, and to attack 
it with interest and determination, a solution is assured. 

57. Walls of Cylindrical Tanks. — The walls of cylindrical tanks 
are invariably built in st rakes of sheeting, the circumferential 
seams being single-riveted lap joints. 

The basis on which the sheeting is designed is that referred to 
in text-books on applied mechanics as the " theory of thin cylinders " ; 
and this is so simple and obvious as to need no detailed discussion 
here. It is assumed that the liquid pressures, acting radially 



236 



TANK CONSTRUCTION 



outwards, are resisted by direct tension in the ring of sheeting, as 
indicated in Fig. 156 ; and this leads to the relation — 

pd = 2tf; 

in which p is the intensity of the liquid pressure in pounds per 
square inch ; d, the tank diameter in inches ; t, the plate thickness 
in inches ; and /, the tensile stress in the sheeting in pounds per 
square inch. 




Fig. 156. 
The relation may be stated in the form — 

and from this a convenient rule may be obtained for estimating 
the thicknesses of the various strakes to a first approximation, in 
preparation for the actual design. 

Expressing p a.s h I — ^j lb. per sq. in., where h is the liquid 

head in inches (taking the contained liquid as of weight equal to 
that of water), and substituting this value for p, the expression 
may be written — 

62*5 // d 



t = 



2/ X 1728" 



Assuming that one-third of the plate area will be cut away in 
rivet-holes, / must be increased in the ratio 3:2; and if the head 



CYLINDRICAL TANKS 237 

and diameter be expressed in feet instead of in inches (their symbols 
being altered to H and D respectively to denote the change), the 
expression becomes — 

^ ^ 62-5 H D X 144 X 3 

2/ X 1728 X 2 

Lastly, taking /as 7*5 tons per sq. in., and expressing the plate 
thickness in sixteenths of an inch (represented by t-^^) — 

, _ 62-5 H D X 144 X 3 X 16 
^^ ~ 2 X 7-5 X 2240 X 1728 X 2 

^ 5HD ^ H D . 

~ 1344 ~ 268-8 ' 

which, for simplicity in use, may be taken as^ 

t -"^ 

^^ 270 

As an example, if H = 27 ft., and D = 100 ft. — - 

27 X 100 
^^ 270 

whence the plate thickness needs to be I J = | in. 

Obviously, the plate thickness necessary will depend upon the 
diameter and pitch of the rivets ; and hence, the thicknesses estim- 
ated from this rule will need revision — and perhaps amendment — 
after the riveting has been designed. It is convenient, however, 
to have some dependable idea as to the plate thickness when de- 
signing the riveting, and for this purpose the rule is likely to be of 
service. 

Now, the diameter is fixed and definite for any given case, but 
a question arises as to what shall be regarded as the proper liquid 
head governing the thickness of a strake. The pressure intensity 
may be taken as varying uniformly from zero at the surface to a 
maximum at the floor level ; and consequently there will be an 
appreciable difference between the intensities at the top and 
bottom of a 5-ft. strake, even low down in a tank of considerable 
depth. 

The usual practice is to design each strake for the pressure 
intensity at its lower edge (except that no strake is permitted to 



238 TANK CONSTRUCTION 

be less than J in. in thickness), but a httle consideration will show 
that this is unnecessarily severe and extravagant. 

Consider a strake of sheeting, of height b, subjected to internal 
pressures as indicated in Fig. 157, the pressure intensity varying 
uniformly from p^^ at the top to p2 ^-t the bottom. For uniformity 
of stress in the sheeting the thickness should vary directly with 
the pressure intensity (assuming the tank diameter constant) ; 
but this is obviously impracticable, and hence the question arises 
as to what pressure intensity should be taken in estimating the 
thickness for the complete strake. 

Clearly, a thickness based upon the full permissible stress for 
the pressure intensity p^ at the top of the strake would be insuf- 
ficient at any lower level ; while a thick- 

— ' ^ 1 ness similarly deduced for the pressure 

\ intensity p2 at the bottom of the strake 

^. would be wasteful in that practically 

\. none of the material would be working 

^ I up to its accepted limit of permissible 



' stress. 



"^ I Here, however, it should be observed 

that the theory of thin cylinders does 

I not take into account the assistance 

which must inevitably be rendered to 



p2 the ring or strake by a diaphragm or 

-p,^ ,.„ end; nor does it allow for the effects 

of variations in the straining actions 
applied to the material by reason of variation in the pressure 
intensity. The lowermost strake of a cylindrical tank wall is 
fastened securely to the tank floor by means of the bottom curb; 
and since this must prevent the material at and near the lower 
edge of the strake from taking any appreciable strain under load, 
it follows that this material cannot be severely stressed. As to 
how far up the strake this restraining influence extends it is difficult 
to say ; and any attempt to form an estimate by analytical methods 
must of necessity be based upon assumptions which would probably 
not be realised to an equal degree in any two actual structures. 
Possibly some information might be obtained from observations 
with the aid of extensometers apphed to the sheeting of actual 



\ 



CYLINDRICAL TANKS 239 

tanks under all conditions of loading and freedom from load ; but 
even then it is likely that the influences of workmanship and tem- 
perature changes — it takes some time to fill or empty a tank of 
even moderate dimensions — would so obscure the results as to 
prevent them from yielding reliable evidence with regard to the 
assistance rendered by the floor to the wall sheeting. But even 
though no precise and practically acceptable estimate may be 
possible as to its extent, it is obvious and undeniable that the 
lowermost strake of the wall sheeting in a tank of the usual and 
ordinary construction cannot fail to receive assistance from the 
floor with which it is connected ; and the object in drawing atten- 
tion to the fact here is to adduce qualitative rather than quantitative 
evidence in support of a suggestion which will be offered presently 
with a view to effecting economy in the lower strakes of cylindrical 
tank walls. 

From similar reasoning it will be seen that, in the higher strakes, 
the lower portions of any strake will receive assistance from the 
upper portions of a thicker strake immediately below. After all, 
the question is largely one of elastic strains under load; and two 
pieces riveted together so securely as are the adjoining strakes of 
a cylindrical tank wall at the circumferential seams cannot take 
appreciably different strains. Moreover, at the circumferential 
seams there is a double thickness of material in the lap joints ; 
and this must surely exercise a favourable influence upon the 
stresses in the upper strakes— though (as will be seen presently) 
the point is of less practical importance in the upper strakes than 
in those near the floor. 

Let us imagine the strake of Fig. 157 entirely free from 
restraint as regards horizontal motion due to elastic strain at an}'' 
level ; and let us also ignore any assistance which may be rendered 
by the upper (and less severely stressed) portions to those below. 
Then it may be supposed that the strake will be subjected to a 
tension varying uniformly in intensity from T^ (= J z£; A^ d) lb. 
per inch of depth at the top, to Tg (= | z^ ^2 ^) ^^- P^^ i^^h of 
depth at the bottom. 

Considering a portion of the strake laid out flat, the conditions 
as regards loading would then be as indicated in Fig. 158, from 
which it follows that the total tensile force acting upon the strake 



240 



TANK CONSTRUCTION 



r/T + T \ 1 

will be \(—^ ^)^\' "^^'hi-^^ i^s resultant may be assumed to 

act in the line Tr, which passes through the centre of gravity of 
the quadrilateral A B C D in Fig. 158. 

Denoting the distance between the resultant Tr and the bottom 
edge of the strake as ^ 6 (where k is, of course, a proper fraction), 

2 T + T 

it is easy to show that k — /x^ I x^ ' ^^^ ^^ ^^® ratio T, : T^ 

3 (J-i + -12) 
be denoted as r (so that Tg = r T^) — 

Now, Tg : Ti : : (1 ze; Ag d) : (^ w A, ^) ; whence ^ = iir)- 




Fig. 158. 

Thus, for the lowermost strake of a tank 30 ft. in depth, each 
strake being 5 ft. in breadth, k will be — 

80 

165 



{(^ + 



25/ -^ V ^ 25/ 



) 



0-485. 



For the next strake above, k will be — 



25 



\v' + 2o;^n' + 2o;i 



25M _ 65 

135 



= 0-481. 



For the next strake above, k will be 0-476; and for the strake 
immediately below the topmost ( i. e. the strake for which r = — j' 

k will be 0*444. 

The practical significance of these results may be seen from a 
numerical example. 



CYLINDRICAL TANKS 24 I 

Consider the lowermost strake (5 ft. in width) of a tank 100 ft. 
in diameter and 30 ft. in height, assuming the tank filled to the 
brim with water or other liquid weighing 62*5 lb. per cub. ft. 

The average intensity of tensile loading may be taken as — - 

Ti + Tg _ 62-5 X 27-5 X 100 X 12 
2 ~ 2 X 144 

= 7161 lb. per inch of height. 

If the over-all width of the strake be 60 in., only about 55 in. 
will be subjected to direct tension from its own loading, about 
3I in. being covered by the bottom curb, and ij in. at the circum- 
ferential seam connecting this strake with that above. Hence, 
the total tensile force acting upon the plate may be taken as — 

Tr = ^ X 55 = 176 tons. 
2240 ^^ I 

On the basis of the rule for strake thickness deduced in pages 
236 and 237, and taking H as 27-5 ft. (i. e. above the middle of 
the strake) — 

^16 = -^-^ = 10, giving a thickness of f in. 

The resultant of the tensile forces acting at a height of 0*485 h 
= 0"485 X 60 in. = 29'! in. above the bottom of the strake, the 
eccentricity of leading will be 30 — 29*1 = 0*9 in. 

The effective cross-sectional area of the strake to resist tension 
may be taken as f x 60 x f = 25 sq. in., and the section modulus 

as — 

2 I 5 X 60 X 60 

- X ^ X 5 = 250 m. 

36 8 ^ 

Hence, the stresses at the extreme fibres would appear to be — 

•^ ^ \2S 250/ 25 -^ 250 / 't ^ o> 

i. e. 6*41 tons per sq. in. at the top ; and 7*67 tons per sq. in. at 
the bottom of the strake. 

The foregoing discussion and calculation take no credit for 
the assistance which the strake sheeting will receive through being 
riveted to the bottom curb. If the lower edge of the flat plate 

R 



242 



TANK CONSTRUCTION 



considered above were held against extension by sensibly rigid 
stops, as indicated in Fig. 159, it might well be claimed that the 
additional stress calculated on the basis of eccentric loading should 
be ignored in designing; and a consideration of the conditions 
under which the lowermost strake of a cylindrical tank wall must 
act will show this as a very moderate claim. 

It is suggested, therefore, that a strake may be designed on the 
basis of a liquid head measured above a level midway between 
its upper and lower edges, as regards both plate thickness and 
riveting. Had the full 30 ft. head been taken for the example 
considered above, the estimated plate thickness would have been 




Fig. 159. 

at least 10 per cent, in excess of that proposed, showing an appreci- 
able saving for the suggested method. 

As regards the upper strakes, it will be seen that the eccentricity 
of the resultant tension is greater, while the assistance received in 
restraint is probably less, than for the lowermost strake ; and 
hence the advantage to be gained may be less. But the loading on 
the upper strakes is much lighter, and the difficulties of designing 
economically are much less, than for those near the bottom of a 
tank. 

For obvious reasons, no strake should be less than J in. in 
thickness. 

The method of designing a strake and its riveting may be shown 
best by means of a typical example. 

Consider the case of the lowermost strake for a tank 100 ft. 
diameter and 30 ft. in height, as above, the plate thickness having 
been already estimated provisionally as | in. 

A rivet | in. diameter has a permissible resistance of 579 tons 



CYLINDRICAL TANKS 243 , 

in double shear, and 6*02 tons in bearing in a f in. plate. For a ] 

total tension of 176 tons, therefore, the net number of rivets re- ' 

176 
quired will be — ^ = 31 ; and as these are to be field rivets, the 
^ 579 

number should be increased to about 40 in view of the serious I 

consequences which might arise through a defect in one of these ' 

seams. 1 

With a pitch of 3 X | in. = 2| in., there is accommodation 
for, say, 57 in. -^ 2| in. = 21 rivets in a single row; and hence, 
a double-riveted butt joint, with double covers J in. in thickness, 
will be both suitable and economical. 

On the provisionally estimated plate thickness, the net area for 
resistance to tension will be | X {60 — (22 x |)} = 25*47 sq. in., 1 

giving a direct stress of — f- = 6*9 tons per sq. in., which is ' 

satisfactory. 

Again, consider the lowermost (5 ft.) strake for a tank 150 ft. ! 

in diameter and 35 ft. in height. 

The provisional estimate for the plate thickness will be — 

^ 32-5 X 150 ^ I 

^^ 270 

giving a plate i| in. in thickness. The total tension in the ring i 

may be taken as — 

^ 62*5 X 32-5 X 150 X 55 , 

Tr = — "^ ^^~ ~ ^ = 312 tons. 

12 X 2240 X 2 

312 
The net number of X in. rivets required would be - — =54; i 

and hence, a double-covered butt joint with three rows of rivets ; 

(giving about 64 rivets as against the net 54 required) on each side \ 

of the butt would be suitable. 1 

The net area of plate section at the first row of rivets past the 

edges of the butt covers will be f X {60 — (22 X f)} = 45'8 sq. in., j 

312 . ... I 

giving a direct stress of —^ = 6'8 tons per sq. in., which is satis- i 

factory. 

From the foregoing examples it will be seen that, with large 



244 



TANK CONSTRUCTION 



tanks, the riveting for the lowermost strakes becomes difficult 
owing to the large number of rivets for which accommodation must 
be found. Sometimes the diameter of the rivets is increased in 
order to reduce their number; and this, within reasonable limits, 
is good practice, since the shearing resistance of a rivet varies as 
the square of its diameter. Rivets more than i in. in diameter 
are apt to be very troublesome to close properly, however, especially 
out in the field ; and it is by no means certain that any real saving 
is effected by their use. 

With regard to the suggestion sometimes put forward that the 
vertical seams should be lap joints, it will be seen that such a course 
would be the reverse of advantageous in practice. Since the 

resistance of each rivet would be 
practically halved by reason of its 
being placed in single shear, the total 
number of rivets in the joint would 
probably not be less than with the 
double-covered butt joint ; while the 
slight saving through the omission 
of the butt covers would almost 
certainly be more than cancelled by 
the necessity for thinning and setting 
the plate comers — an extremely 
troublesome matter with such heavy 
plates and very long laps, and likely 
to cause trouble with such high pressures. 

Cases may arise in which a saving in the plate thickness of a 
strake is obtainable by arranging the rivets on some such lines as 
those indicated in Fig. i6o. The increased pitch at the first row 
of rivets past the edges of the butt covers causes less reduction in 
the plate section, and thus may render permissible the use of a 
plate thickness which might otherwise be difficult to justify. It 
will be clear, however, that the calculated increase in the plate 
resistance obtainable by such means cannot be very great ; while 
the distribution of loading among the rivets, as well as over the 
plate section, is highly problematical. Such methods should be 
used very sparingly; and it is an unfortunate fact that the 
only cases in which they might be of real assistance are just 




Fig. i6o. 



CYLINDRICAL TANKS 



245 



those in which the need for rehabiUty is greatest, and the con- 
sequences of some relatively slight deficiency likely to be most 
serious. 

The use of a pitch much less than three times the rivet diameter 
is undesirable not only because it involves a large reduction of the 

Rivet Areas (in HONOftoTHt. of a a<j in.^ REcau;REO 
FOR aSft Strake, per foot of tank diameter. 

Z 4 C? fi 'O 12 t4 /S, f3 30 ZZ »>■ X, Z? 3o 



15 



20 



25 



23 

30 



55 



40 



45 



\ 



h 




WtlQMT OF CONTAINED l.l<aUIO " &Z-S lb PER Cua FT 

I I I I I I I I I I I I I I I I I I I 
PITCH OF RIVETS ASSUMED AO 3 J^ OIAMETE.R 



RIVET RESISTANCE TAKEM A& 9-€>S5Tt>N3 PER SO 

I I I I I I I I M I 1 I I I 



PERMISSIBLE STRESS IN PLATES «« 

I I I I I I I I I I i 
^•5 TONS »=»eR S<5. IN. NCT 



\ 



/ 2 3 -^ 5 6 7 a 

Plate THicKNesses^NTMOusANOTHS of an inch) 

RBQUII^EO PER FOOT OF TAJ^•K. DIAMETER 

Fig. i6r. 



plate resistance (thus necessitating the use of thicker plates), but 
also because it tends to increase the difficulties of riveting by 
reducing the clearance spaces for the tools. 

Trouble may be saved in designing by the construction of a 
diagram such as that shown in Fig. i6i. 



246 TANK CONSTRUCTION 

The principle on which the diagram is constructed will be clear 
from the following notQ3. Since 

— ^^ — H D X 1000 _ TT -pj / 25 \ 

^i« - 270 ' ^i««o ~ 270 X 16 ~ -^ ^ Vio8> 

•*• ^1000 = H ( ^o) per foot of tank diameter. Where 

^1000 =10, H = = 43 ft. nearly. Total tension in strake 

25 

62-5 H D X 5\ ^ 

— tons. 

2 X 2240 / 

Rivet area required = A = H D ( ~ ^— ^ — ) sq. in. 

^ \2 X 2240 X 9'625/ ^ 

hundredths of a sq. in. per foot of tank diameter. Where 

. TT 20 X 17,248 o r^ 1 

Ainn == 20, H = ^- ~- = 28 ft. nearly. 

^^^ ' 125 X 100 ^ 

Modifications, refinements and approximations will doubtless 
suggest themselves, both for simplifying the construction of the 
diagram and for increasing its usefulness. 

Since the rivet areas required have been estimated on the basis 
of shearing resistance in double shear, riveting provisionally 
designed from Fig. 161 requires investigation with regard to 
bearing resistance ; while appropriate increase in the rivet areas 
must be made if the rivets are to act in single shear. 



CHAPTER VIII 

ELEVATED CYLINDRICAL TANKS 

58. Elevated Cylindrical Tanks. — An elevated cylindrical tank, 
supported upon a substructure of braced steelwork, may have 
either a flat floor or a dished bottom, as indicated in Fig. 162. 

The flat floor needs a system of deck beams to support it, and 
this fact is often put forward as a disadvantage of the flat floor 





FLAT BOTTOMED 



SE&MENTAL 

Fig. 162. 



SPHEROIOAL 



by those who favour the dished bottom. It will be seen, however, 
that with the flat floor the problems of design are simple, the type 
of work involved in manufacture comparatively straightforward 
and cheap, and the fabricated material free from special difftculties 
as regards transport and erection— all factors tending towards 
economical and rapid production of the structure as a whole. 

247 



248 TANK CONSTRUCTION 

The dished bottom adds to the capacity of a tank, and may be 
considerably hghter than the flat floor with its deck beams ; but 
its action is hkely to be somewhat uncertain with changes in the 
head of the contained Hquid, while the work involved is obviously 
expensive, both in manufacture and erection. Besides the trouble- 
some and costly work of bending and riveting the plates, two 
rather serious practical difficulties are introduced by the dished 
bottom. First, the connection of the bottom with the cylindrical 
wall of the tank proper is awkward, and requires great care in 
design and fitting to ensure adequate strength and tightness against 
leakage ; and second, the support of the tank as a whole becomes 
J complicated through the interference of 

'""'^'1 ^- the suspended bottom. 

'TX^ I ~/^- 59- Flat-Floored Tanks. — The roofs 

/ j sT^cHioNs ^ ^^^ walls of elevated cylindrical tanks 

/ I I \ with flat floors may be of design and 

> . I ! r construction similar to those for tanks 

\ ' staJhions I / which stand upon a flat base at or near 



"^y I ^^ ground level. 



The floor-plates may be arranged on 
a lay-out similar to those suitable for 
ordinary tanks, as already described, but 
the plates must be of such thickness as will permit of their spanning 
between the supporting joists without exceeding the permissible 
limits of stress. The methods of treatment from this point of view 
are, however, not materially different from those already described in 
connection with the flat floors of elevated rectangular tanks ; and 
hence, no further discussion is necessary beyond pointing out that 
the joists supporting the floor plates should be arranged to lie at 
right angles to the main (long) seams, and the transverse seams 
placed where they will not be subjected to stresses likely to cause 
them to open sufficiently to become leaky. 

Elevated tanks are seldom more than 40 ft. (usually they are 
in the neighbourhood of 20 ft.) in diameter ; and hence the author 
is of opinion that only four stanchions are necessary for their sup 
port, arranged at the corners of a square, as indicated in Fig. 163 
By this means, the supporting structure may be braced to form a 
square tower, with great strength and stiffness in resisting the 



ELEVATED CYLINDRICAL TANKS 



249 



overturning actions of wind pressures obtainable by simple and 
economical means. 

An arrangement for the floor joists and beams on this basis, 
suitable for all ordinary cases, is shown in Fig. 164. The tank 
may overhang the outermost joists by a distance equal to 075S, 
where S is the spacing (centre to centre) of the joists in the body 
of the floor. In these parts, the cylindrical wall will act as a girder 
in assisting to support the floor and its loading. 

The tank should be adequately anchored to the supporting 
structure to prevent movement and overturning under the action 




plan of joist deck 
Fig. 164. 




Fig, 165. 



of wind pressures. There is little danger of such movement or 
overturning while the tank is full, or even partly full ; but when 
the tank is empty it may not have sufflcient stability by reason of 
its own mass to resist a sudden and violent wind storm, and the 
anchorage should therefore be designed on the basis of the empty 
tank, with a reasonable margin to provide for dynamic effects. 

60. Conical Bottoms. — It is a comparatively simple matter to 
deduce mathematical expressions for the stresses in a dished bottom 
of any given shape — conical, hemispherical, segmental or spheroidal 
— if suitable conditions be assumed and disturbing influences 
ignored; but it is open to question as to whether the stresses in 
an actual dished bottom, manufactured under ordinary commercial 
conditions, and loaded as such structures must be in real life, bear 



250 



TANK CONSTRUCTION 



a reasonably close relation to those estimated on the basis of any 
particular set of assumptions. 

Consider, for instance, the conical bottomed tank indicated in 
Fig. 165, containing water (or other liquid of equal density) to the 
depth shown. 

Stresses due to Suspension. — Taking a horizontal section, such 
as AA, and imagining the lower portion of the cone (with its load- 
ing) detached from the rest, the conditions would be as indicated 
in Fig. 166. 



(h*S) 





Fig. 166. 



Fig. 16' 



The weight of the contained hquid will be — 

and this may be regarded as the weight to be supported, for the 
weight of the sheeting itself will usually be insignificant in com- 
parison with that of the contained liquid— at least when the tank 
is fairly full. 

As the entire weight must be supported around the rim AA, 
where the circumference is tt a\, the vertical force (in pounds per 
inch of circumference) will be — 



V 



= W - :r ^, = ^^V^ (3 h, + h,) ^^d,=^^(3h, + h,) 



12 '- ^ • -' ^ 12 

all linear dimensions being in inches, and lu in pounds per cub. in. 



ELEVATED CYLINDRICAL TANKS 25 1 

For water, this becomes — 
V = ^1 (3 K + K) ^^^l^'^ 13 = 0-003 ^1 (3 K + K) lb. per inch. 

Resolving V horizontally and tangentially, as in Fig. i66 — 

H = V. tan fj> = 0-003 d^ (3 /^^ + h^) tan <^ lb. per inch. 
T = V. sec <^ = 0-003 di (3 hi + //g) sec <^ lb. per inch. 

Now, T must be resisted as a tension in the conical sheeting, 
in straight lines radiating from the apex ; and hence, the required 
thickness of the sheeting, for any given stress, may be readily 
estimated. 

That T will be a maximum at the junction of the cone with the 
tank proper may be easily seen without calculation ; for T is propor- 
tional to i ^if/^i H — ^-)\, i' e. to the area of the rectangle P Q R S 

in Fig. 167 — which obviously reaches its maximum at the upper 
extremity of the cone. 

As an example, in a conical bottomed tank, the cylindrical 
portion being 20 ft. diameter and 20 ft. in height, and the drop of 
the cone 10 ft., the magnitude of the tension will be — 

T = 0-003 X 240 (720 + 120) 1*414 = 0-003 X 240 X 840 X 1*414 
= 855 lb. per inch of circumference. 

At a permissible stress of 7-5 tons per sq. in. {i. e. 16800 lb. per 
sq. in.), and reckoning upon a loss of one-third of the plate section 
in rivet holes, the required plate thickness (to resist this tension 
only) would be — 

^ ^ 16800 ^2 ^'^^ '^^' practically, ^\) inch. 

The horizontal component (H) of the supporting forces has- yet 
to be dealt with and provided for. It is sometimes stated that the 
resistance to this component, acting with the resistance to the 
tension T to produce the necessary vertical reaction, inevitably 
causes an inward pull to act upon the connection between the cone 
and the tank proper ; but a little consideration will show that this 
is not necessarily so. 

Obviously, the horizontal component of T must be resisted. 



252 



TANK CONSTRUCTION 



and if the cone were supported by a series of separate strips, as 
indicated in Fig. i68, the connections of those strips would un- 
questionably be subjected to the action of a horizontal inward 





Fig. i68. 



Fig. 169. 



(radial) pull all round the circumference. This aspect of the matter 
is, however, arrived at on the basis of simple suspension only, and 
the conditions would be exactly the same if the downward load 




Fig. 170. 




Fig. 171. 




Fig. 172. 



were due to the weight of a solid body instead of liquid, standing 
upon (or suspended from) the junction of two flexible cords, as in 
Fig. 169. 

If the cone were rigid, and supported as shown in Fig. 170, the 
loading applied to the supporting substructure would be vertically 



ELEVATED CYLINDRICAL TANKS 



253 




Fig. 



173. 



downward; and this fact provides a simple means for preventing 
the troublesome inward pull which would otherwise act upon 
the connection. To simply flange the 
thin sheeting of the cone, as indicated in 
Fig. 171, would not be sufficient, for the 
tendency of the tensions would be to 
straighten out the flanging to the conical 
form, and the inward pull would then 
act as before ; but if a ring were pro- 
vided at the flanging, as shown in Fig. 
172, sufficient to prevent distortion of 
the flanging, the difficulty would be met. 
The arrangement of Fig. 172 is intended 
to illustrate the point in principle only, 
and not necessarily to indicate the 
manner in which the joint may be con- 
structed in practice ; several other ways — perhaps more convenient , 
and not less effective— are available for securing the desired results, 

and these will doubtless 
suggest themselves readily. 
Hoop Tension. — In 
addition to the conical 
tensions caused by the 
suspension of the bottom, 
the liquid pressures must 
be resisted by horizontal 
hoop tensions in the 
sheeting. 

Consider the ring of 
sheeting between two 
'Choop) horizontal sections BB and 
CC in Fig. 173. This ring 
has to support the hollow 
circular column of liquid 
which stands upon it ; and 
the conditions as regards 
loading and support will be seen clearly from Fig. 174, which shows 
the ring (with the column of liquid which it supports) detached 




254 TANK CONSTRUCTION 

from the rest. The ring of sheeting is supported solely by the 
conical tensions Tp as shown, Tp being such part of T (Fig. i66) as 
is due to the hollow column of liquid standing upon the ring BB CC. 

If the inclined depth (BC) of the ring be / inches, the normal 
pressure P acting upon a strip of it i in. in length (perpendicular 
to the plane of the paper) will be wh-^ I. The magnitude of Tp 
will be {wh-^ I tan </>) ; and the horizontal component H will be 
[wh-^ I sec cf)). 

This horizontal pressure, acting radially outwards all round the 
ring, will cause a total bursting force of {whi d^ I sec cf>) , which 
must be resisted by tension across two sections of the ring — similar 
to those shown blacked in Fig. 174 — cut by a diametral plane. 
If the thickness of the sheeting be t inches, and the tensile stress 
/ lb. per sq. in. — 

2 It f = wh-^ d^ I Sec cf) ; whence — 

_ whi di Sec (f> ^ , ^ r _ whi d^ Sec </> 

t — 7 '. and I / — 

2 A 2t 

The hoop tension, being proportional to the product h^ d^, will 
clearly be a maximum at the top of the cone. 

For the example previously considered, and with the same 
conditions — 

_ 62-4 X 240 X 2 40 X i'4 i4 X 3 
~" 1728 X 2 X 16800 X 2 

= 0*13 (or a trifle over J) inch. 

A thickness of ^V in. was found necessary for the conical tension ; 
but in practice, to allow for contingencies, and to provide a 
reasonable margin for corrosion, it would probably be well to use 
sheeting J in. or -^\ in. in thickness. 

61. Hemispherical Bottoms. — With a hemispherical bottom, the 
tensile stress, due to suspension, across a section cut by a hori- 
zontal plane, may be estimated on a basis similar to that employed 
for the conical bottom. 

Consider the conditions at the section A A in Fig. 175. 

The weight of the contained liquid will be (approximately) — 



W 



= -^,^(/., + ^^^)z. = -^-^'(2^ + /g. 



ELEVATED CYLINDRICAL TANKS 



255 



The length of the rim (circumference) at AA being tt d-^, the 
vertical force to be resisted will be — 



V = 



_ TT d^ w 



^1 w 



g — (2 K + K) -^ 7rdi= -^— (2 Ai + h^) 

= 0*0045 di (2 h-^ + ^2) lt>. per inch of circumference. 

Resolving V horizontally and tangentially, as in Fig. 175— 

H = V tan cf) = 0-0045 ^1 (2 /h + h^) tan <f>. 
T =Y sec cf) = 0-0045 ^1 (2 /^i + A2) sec </>. 





In this case, Sec (j> varies from section to section ; and near the 
bottom of the bowl sec cf> will be very large. Hence it is well to 
pay particular attention to the lower portions in designing, especially 
if there be much riveting. Sometimes a stout cap plate is used at 
the extreme bottom ; and in many cases the bowl is partially sup- 
ported by a central pipe — or "riser" — of considerable strength 
and stiffness, based upon the foundations. 

Hoop Stresses. — Considering a ring of sheeting between two 
horizontal sections such as BB and CC in Fig. 176, there are two 
actions causing hoop stresses in the bowl — 



256 



TANK CONSTRUCTION 



(i) The normal pressures of the hquid, as in the case of the 

conical bottom ; and 
(2) the resultant of the suspensory tensions T^ and Tg, which are 

no longer in line here as they were in the conical bottom. 

The first of these actions will cause hoop tension, precisely as in 
the case of the conical bottom, the intensity of the stress being — 

wh i ^1 Sec <^ _ 0-0361 hidi Sec <f> 



ft = 



2t 



2t 




RESULTArsrr a 

T S«NX3( 




Fig. 177, 

The second action will cause hoop compression, the magnitude 
of which may be estimated as follows. 

Consider the forces as shown — the curvature being exaggerated 
for the sake of clearness — in Fig. 177, T^ and Tg being estimated 
on the same basis as that employed for the conical bottom, but 
each acting, of course, tangentially to the sheeting of the bowl at 
the level of its own section plane. 

As the angle a is made smaller and smaller, Tj and Tg become 
more and more nearly equal ; until, with a very small, T^ will be 
sensibly equal to Tg. The radial (inclined) component of T^ will 

b^ • Qi = Ti Sin - ; and the radial (inclined) component of Tg 



ELEVATED CYLINDRICAL TANKS 257 

will be : Q2 = Tg Sin -. With - very small (since the circular 

measure of a very small angle is sensibly equal to its sine), the 
radial (inclined) resultant of T^ and Tg will be — 

1 Sm - ^ T, a. 
2 ^ 

Resolving this resultant horizontally and tangentially, the 
horizontal component will be — 

H(A<x>p) = Ti a Sec <^. 

This force acts upon a length of sheeting equal to BC = R a ; 
and hence — 



H 



(hoop) 



_ Tj Sec <^ 



Tp — - lb. per linear inch. 



Acting radially inwards upon the ring all round it, this will 
cause a compression in the material at each pair of sections cut 
by a diametral plane. 

Thus — 



, r T^\ d-. Sec d) 

2 tfc = -^-^ — ^ ; 



R 



whence — 



and — 



r Ti d-i Sec <f) „ 
fc = V, lb. per sq. m.. 



2Rt 



, Ti d-i Sec <t> . , 
t = — — Y5-f — inches. 

2R/c 

But Ti = 0*0045 ^1 (2 h^ + h^) sec <^ ; and substituting this value 
for Ti in the expression for fc — 

f - Q-QQ45 ^1^ (2 Ai + ^2) Sec^ <^ 

The net hoop tension, therefore, will be — 

/. r _ f Q'036i /?! di S ec <^ 0*0045 ^^^ (2 /j^ -j- Ag) Sec^ <f>'] 

lb. per sq. in. 



258 



TANK CONSTRUCTION 



For the hemispherical bottom, R = i ^ ; and Sec <^ = R : i ^^ = 
d : d^. Substituting these values for R and Sec <j>, the expression 
for the net hoop tensile stress becomes — 



f'-fc = 



9 d 

2000/5 



(2 h^ - h^). 



At the junction of the bowl with the tank proper, however, the 
volume can be expressed more accurately; and hence, for this 
level only — 

Ti = 0-003 d{3h-{~ d); 
giving— 

ft-fc = -^^l7,h-d). 
'' ^ 1000 t ^^ ' 

When the expression for net hoop tension, upon evaluation, 
gives a positive result, the hoop stress is tensile; and when the 

result is negative, the hoop stress is 
compressive. An example of the latter 
condition is illustrated in Fig. 178, the 
bowl being only partially filled. Above 
the water level there is no outward 
normal pressure, and hence the hoop 
stress is entirely compressive, tending 
to cause buckling and crumpling of the 
material — under which action riveted 
seams in the spherical sheeting are 
hardly likely to remain tight against 
leakage. Even for some distance below 
the surface level, the hoop tensions 
^\ill not be sufficient to completely 
nullify the hoop compressions. 
The bowl might, of course, be stiffened against inward buckling 
by means of curved ribs radiating outwards from the extreme 
bottom, and stayed by horizontal struts or rings— somewhat on the 
lines suggested for the trough-bottomed rectangular tank in Fig. 113. 
62. Dished Bottoms Generally. — The segmental bottom, and also 
the spheroidal bottom may be investigated for stresses on lines 
exactly similar to those described and illustrated above, and there 
]s, consequently, no need for further discussion of them. 




Fig. 178. 



ELEVATED CYLINDRICAL TANKS 259 

The construction of dished bottoms for tanks — conical, hemi- 
spherical and the rest — in this country is a matter of some difficulty, 
and seems likely to remain so. While the demand is so small, the 
cost of forms renders the work so expensive as to be practically 
impossible ; and until the cost can be much reduced by the acqui- 
sition of stock and standard forms in tank yards generally, the 
demand cannot well increase. So there is a kind of deadlock. 

Moreover, the work of erection is unquestionably of a very 
troublesome and costly nature, and it is doubtful whether any real 
saving could be effected in ordinary cases (even if manufacturing 
costs were reduced considerably) by the adoption of dished bottoms 
in place of fiat bottoms — which latter is the form usually employed 
for elevated cylindrical tanks in this country. 

Under these circumstances, it is neither worth while nor likely 
to be of practical assistance to give details of construction for 
dished bottoms ; for such details as could be suggested are not in 
general acceptance, nor have they been used in a sufficient number 
of cases to warrant a claim to general acceptability. 

63. Stibstruchires and Foundations. — -The design for the stan- 
chions and bracing need not concern us deeply here, for it is a 
matter of ordinary structural steelwork. 

Obviously, the weight of the entire tank and its contents will 
be uniformly distributed over the four stanchions; and for the 
horizontal loading due to wind pressures the tower may be re- 
garded as consisting of four framed cantilevers, anchored to the 
foundations. 

At each panel point, the four stanchions should be connected 
by horizontal diaphragm braces capable of acting either as ties or 
struts as circumstances may require; but inclined bracings in the 
diagonal planes should not be necessary in ordinary cases. 

It will be clear, upon consideration, that a tower composed 
of four stanchions is much more simple and straightforward in con- 
struction than one composed of six or eight stanchions; and its 
action is correspondingly more definite, so that its design may be 
economical without fear of the peculiar and destructive effects 
which are so often set up, through the influences of manufacture, 
in structures of a more or less indeterminate character. 

In designing the foundations for such structures, it frequently 

s 2 



260 TANK CONSTRUCTION 

happens that the most severe conditions obtain when the tank is 
empty, the structure then possessing comparatively httle stabihty 
of its own wherewith to resist the overturning actions due to wind 
pressures. 

The necessary stabihty may be provided by securely fastening 
the concrete foundation blocks (which must, of course, be of 
sufficient weight to resist the uplifting tendency, with an adequate 
margin — usually from 50 to 100 per cent. — to allow for dynamic 
effects) to the stanchion shafts by means of anchor plates embedded 
in the foundation blocks and firmly bolted to the stanchion bases. 



INDEX 



Action of curbs and rails, 136 

of sheeting, 34, 120, 128 

of trough bottoms, 183 

Advantages of cyUndrical tanks, 52 
Allowances for corrosion, 75 
Alternations of stress, 108 
Anchorage for elevated tanks, 249, 

260 
Appearance, factors influencing, 57 
Arrangement of circular floors, 218 
of curbs, rails and stiffeners, 

127, 130 

of cylindrical tanks, 204 

of floor joists, 83, 91, 249 

of rivets, 19 

of sheeting, 39, 58, 60, 68, 71, 

179 

of vertical stiffeners, 127, 164, 

205, 209 

Basis for design, 2 
Bending plates to curves, 34, 216 
Bottom corner connections, 180 
curbs, marking and holing, 

233 

, trough, action of, 183 

, , construction of, 188, 190, 

193 
Bottoms, conical, 35, 52, 247, 249 

, dished, 34, 52, 59, 258 

, elliptical, 58, 62, 183 

, flat, 61, 247, 248 

, segmental, 61 

, trough, 57 

Bracing for stanchions, 202 

for trough bottoms, 200 

Bulkhead riveting, 197 
Bulkheads, 194, 201 
Bunkers, 61 

Cantilevered walls, 86 

, sheeting thicknesses for, 90 

Cast-iron tanks, 5 

Caulking, 31, 77, 82, 86, 181, 225 

Clearances for riveting, 18 



Coal bunkers, 61 
Concrete tanks, 5, 169 
Conditions of loading, 28 

of working and permanence, 29 

to be met by riveting, 6 

Conical bottoms, 35, 52, 247, 249 
Construction, materials of, 3 

of bulkheads, 195 

of trough bottoms, 188, 190, 

193. 197 
Contingencies, margin for, 30 
Continuity of sheeting, 165, 180 

of supports, 168 

Continuous curbs, 147 

with varying sections, 157 

Contraflexure points in curbs and 

rails, 152 
Corner, bottom, connections, 180 

pieces, 181 

ties, 160 

Corrosion, 29, 165, 181 

— — ■, allowances for, 75 

Cost of substructure, 3 

Countersunk rivets, faulty, 15 

Cubical tanks, 36 

Curb connections, 145, 155, 157, 159, 

160, 163 

corners, forged, 155, 157, 159 

, gusseted, 140, 142 

, top, as wall stay, 94 

Curbs, action of, 136 

, aided by sheeting, 140, 144 

, arrangement of, 127 

, design of, 143 

, marking and drilling, 233 

, spliced, 155 

Curved sheeting, 34, 216 

templets, 228 

Curves, large, setting out, 230 
Cylindrical tanks, advantages of, 52 

, economical proportions, 46 

— , elevated, 34, 52, 247 

, floors of, 51, 217, 223 

, general arrangement oj, 

204 



261 



262 



INDEX 



Cylindrical tanks, roofs for, 205 

, roofed, 48, 50, 55, 56 

, with dished bottoms, 52, 

68, 258 

walls, 235 

, design of, 238 



Depth, effective storage, 53 
Design of bracings, 201 

— of bulkhead stiffeners, igy 

of bulkheads, 194, 201 

of corner connections, 157 

of corner ties, 163 

of curbs, 143 

of cylindrical walls, 238 

of raking stays, 178 

of rectangular floors, 71 

of rectangular tanks, 154 

« of transverse ties, 145 

of trough bottoms, 188 

Desirable basis for design, 2 
Determination of rivet diameters, 16, 
22 

of sheeting thicknesses, 74, 97, 

103. 113, 119, 124, 205, 207, 
237, 241, 243, 245, 251, 254, 
257 
Diagram for use in designing, 245 
Diameters of rivets in relation to 

grip, 18 
Dies for flanging plates, 86 
Dimensions of rivet heads, 12 
Dished bottoms for tanks, 34, 52, 59, 

247, 258 
Divergence from economical propor- 
tions, 49, 54, 64 
Drilled holes for rivets, 8, 10 
Drilling bottom curbs, 233 

Economical level for stay rail, 103, 
112, 118 

ordering of material, 228 

Economy of form, 33 
Effective storage depth, 53 
Effects of inferior materials, 4 

of manufacture, 27 

of pressure variations, 107 

of punching holes, 8, 9, 10 

Elastic limit, 26 

Elevated cylindrical tanks, 34, 52, 
• 247 

tanks, anchorage of, 249, 260 

Elliptical trough bottoms, 58, 62, 183 

Erection of floors, 233 

of trough-bottomed tanks, 199 



Faults in riveting, 14, 15 
Field riveting, 13 
Flat-bottomed tanks, 61, 247, 248 
Flat curves, setting out of, 230 
Floor joists, spacing of, 83, 91, 249 

plans, symmetry in, 220 

plates, shaped, 225 

Floors, erection of, 233 

of cylindrical tanks, 51, 217, 

223 

of rectangular tanks, 41, 45, 70 

, rectangular, design of, 71 

, seams in, 76, 81 

-, use of welding in, 234 



Fluctuations of stress, 108 
Forged corner pieces, 181 

corners for curbs, 155 

Form, economy of, 33, 147 
Forms for flanging plates, 86 
Foundations and substructures, 259 
Framing for rectangular tanks, 131, 

135 

for trough bottoms, 187, 200 

Friction in riveted joints, 22 

General arrangement of cylindrical 

tanks, 204 
Girders, walls acting as, 198 
Grip of rivets, 15, 17 

, in relation to diameter, 18 

Gusseted corners for curbs, 140, 142, 

145 

Hemispherical bottoms, 52, 247, 254 

tanks, 34 

Holes for rivets, punched and drilled 
8, 10, II 

, setting out, 7 

Holing bottom curbs, 233 

Hoop stresses in cylindrical walls, 235 

in dished bottoms, 253, 255 

Horizontal rails as wall stays, 100, 

113 

, design of, 147 

, economical level for, 103, 

112, 118 

ties, 131, 134, 144 

, design of, 145 

, trussed and propped, 132 



Inferior materials, effects of 4 
Influences of uneconomical form, 3 
Initial stresses, 27 
Introduction, i 
Importance of appearance, 57 



Factor of safety, 30 



Joggling or packing, 164 



INDEX 



263 



Large radius curves, setting out, 230 
Lengthening due to punching, 9 
' Lengths of rivets for ordering, 15, 17 
Limit of elasticity, 26 
Limits of plate thicknesses, 7 

of rivet diameters, 7 

Loading conditions, 28 

on curbs and rails, 147 

on supports, 174 

on tank walls, 88, 93, loi, 107, 

114, 120 
Local exigencies, i 

Manufacture, effects of, 27 
Margin for contingencies, 30 
Marking bottom curbs, 233 
Materials, inferior, effects of, 4 

, of construction, 3 

, permissible stresses in, i, 25, 31 

, properties of, 26 

, specifications for, 6 

Minimising riveting, need for, 6 
Model for studying trough bottoms, 

187 
Multiple punching, 7 

Need for minimising riveting, 6 

for research, 120, 129, 190 

Nipple punch, 8 

Nominal rivet diameters, 11 

Ordering material, 228 

rivets, 15 

shaped floor plates, 225 

Packing in seams, 83 
Packing or joggling, 164 
Permanence, conditions of, 29 * 
Permissible stresses, i, 25, 31 
Pitch of rivets, 19 
Plate thicknesses, 7 
Plates, bending of, 34, 216 

, shaped, 225 

Plating, action of, 34, 120, 128, 140, 

144 
, arrangement of, 39, 58, 60, 68, 

71. 179 
Plating thicknesses, determination of, 

74, 97, 103, 105, 106, 113, 119, 

124, 205, 207, 236, 241, 243, 

245, 251, 254, 257 

for cantilevered walls, 90 

for heavy pressures, 113 

for stayed walls, 98, 106 

Practical construction of troughs, 197 

design of tanks, 154 

Pressure variations, effects of, 107 



Primary stresses, 26 
Properties of materials, 26 
Proportions of rivets, 12 
Punched holes for rivets, 8 
Punching, effects of, 8, 9, 10 
, single and multiple, 7 

Rack punching, 7 

Rail connections, 157, 159, 163 

corners, bracketed, 157 

, forged, 155 

, tied, 161 

Rails, action of, 136 

, arrangement of, 127, 130 

, continuous, 147, 164 

, , with varying sections, 

157 
, contraflexure points in, 152 

, economical level for, 103, 112, 

118 

, horizontal, as wall stays, 100, 

113 

, loading on, 147 

, spliced, 155 

trussed, 134 



Raking stays, 135, 169, 173, 177 

, design of, 178 

Reaming, 9 

Rectangular floors, design of, 71 

tanks, 34, 42 

, flat-bottomed, 61 

, floors of, 41, 45 

, framing for, 131 

' , roofs of, 39, 44, 142, 166, 

169 



183 



segmental-bottomed, 61 
-, trough-bottomed, 57, 68, 

walls of, 60 
Reinforced concrete tanks, 5, 169 
Relation of rivet diameter to grip, 18 

to plate thickness, 7 

Requirements due to situation, i 
Research, need for, 120, 129, 190 
Ribbed tanks, 166 
Rivet diameters, determination of, 

16, 22 
, limits of, 7 



heads, dimensions of, 12 

, unaxial, 14 

holes, out of line, 8, 9 

, punched and drilled, 

10, II 

, setting out, 7 

diameters, nominal. 11 

resistances, 19 

Riveted joints, friction in, 22 



264 



INDEX 



Riveting arrangement of, 19 

, clearances for, 18 

, faults in, 14 

, for bulkheads, 197 

-, for cylindrical walls, 237, 243 

, for floors and roofs, 217, 224 

, for stiffeners, 129 

, generally, 6 

— — , in floor seams, 81, 224 

, need for minimising, 6 

, yard and field, 13 

Rivets, countersunk, faulty, 15 

, grip of, 15, 17 

, lengths for ordering, 15, 17 

, pitch and arrangement of, 19 

, proportions of, 12 

, specification for, 6 

, subjected to tension, 100, 145 

, weights of, 23, 24 

, with tapered shanks, 13 

Roof sheeting, 214 

Roofed cylindrical tanks, 48, 50, 55, 

56 
rectangular tanks, 39, 44, 142, 

166, 199 
Roofs for cylindrical tanks, 205 
Rules for sheeting thicknesses, 74, 97, 

103, 124, 205, 207, 236, 241, 

243, 245,251,254,257 

Safety factor, 30 
Seams in floors, 76, 217 

in roofs, 216 

Segmental bottoms, 61, 247 
Setting out large radius curves, 230 

rivet holes, 7 

Shallow tanks, 87 
Shaped bottoms, 67 

plates, 225 

Sheeting, acting with curbs, 140, 144 

, action of, 34, 120, 128, 140, 144 

— — , arrangement of, 39, 58, 60, 68, 

71. 179 
, continuity of, 165, 180 

thicknesses, determination of, 

74. 97. 103. 105, 106, 113, 119, 
124, 205, 207, 237, 241, 243, 
245, 251. 254, 257 

, for cantilevered walls, 90 

, for high pressures, 113 

, for stayed walls, 98, 106 

Silos, 61 

Specifications for materials, 6 

Spherical bottoms, 35, 52, 247 

tanks, 34 

Spheroidal bottoms, 247 
Splices for curbs and rails, 155, 



Splices for vertical stiffeners, 165 

Square tanks, 35 

Stability of tank walls, 94 

Stanchions, bracing for, 201 

, torsion in, 202 

Stayed walls, 93, loi, 107, 114, 120 

Staying by horizontal rails, 100, 113 

by top curb, 94 

Stays, raking, 135, 1O9, 173, 177 

, , design of, 178 

Steel plates, bars and rivets, specifica- 
tions for, 6 

Stiffeners, arrangement of, 127, 164, 
205, 209 

, for bulkheads, 197 

, vertical, 120, 205, 209 

Storage depth, effective, 53 

Stress, variations in, 107 

Stresses, alternating and fluctuating, 
108 

, due to hoop action, 235, 253, 

255 
, due to suspension of bottoms, 

250, 254 

, initial, 27 

, permissible, 25, 31 

, primary and secondary, 26, 27, 

28 
Stretch due to punching, 9 
Substructure, cost of, 3 
Substructures and foundations, 259 
Support for ties and trussing, 132, 

145 
Supporting joists, spacing of, 83, 91 
Supports, continuity of, 168 

, loading on, 174 

Suspension of troughs, 197, 202 
stresses in dished bottoms, 250, 

254 
Symmetry in floor plans, 220 

Tapered packings in seams, 82 

rivet shanks, 13 

Tank bottoms, conical, 35, 52, 247, 

249 
, dished, 34, 52, 59, 247, 



249 



254 



-, elUptical, 58, 62, 183 

-, fiat, 61, 247, 248 

-, hemispherical, 52, 247, 



-, segmental, 61 

, trough, 57, 183 

walls, acting as girders, 198 
, cylindrical, 235 

-, design of, 238 



163 Tanks of cast iron, 5 



INDEX 



265 



Tanks of reinforced concrete, 5, 169 

, practical design of, 154 

, ribbed, 166 

Tankwork, weight of, 23 

Templet curves, 228 

Templets for setting out rivet holes, 

7, 8, 216 
Tension in rivets, 22, 100, 144 
Thinned plate corners, 81, 218 
Ties for corners, 160 

, design of, 163 

, horizontal, 131, 134, 135, 144 

, trussed and propped. 



132 



190, 



Top curb as wall stay, 94 
Torsion in stanchions, 202 
Transverse ties, design of, 145 
Trough-bottomed tanks, 57, 183 
Trough bottoms, action of, 183 

, bracing for, 200 

-, construction of, 188, 

193 

, erection of, 199 

-, framing for, 187, 200 

, model for studying, 187 

, need for research, 190 

, suspension of, 197 

Trussed framing, 135 

, support for, 145 

rails, 134 



Unaxial rivet heads, 14 
Uneconomical form, influences of, 3 



Use of welding in floors, 234 

Value of appearance, 57 

Variations in pressure, effects of, 

107 

in stress, 108 

Vertical stiffeners, 120, 205, 209 
, arrangement of, 127, 164, 

205, 209 

Walls, acting as girders, 198 

■, cantilevered, 86 

, cylindrical, 235 

, design of, 238 

, loading on, 88, 93, loi, 107, 114, 

120 
■ — — of rectangular tanks, 60, 70 

, stability of, 94 

, stayed, 93, loi, 107, 114, 120 

, with vertical stiffeners, 120 

Wedge packings in seams, 82 

Weeping, 19 

Weight of rivets, 23, 24 

of tankwork, 23 

Welding, use of, 155, 234 
Working conditions, 29 
Wringing action in stanchions, 202 
Wrought-iron rivets, specification for, 

6 
, use of, 1 4 

Yard and field riveting, 1 3 
Yield point, 26 



Printed in Gri^at Britain by 
Richard Clay & Sons, Limited, 

VARIS garden, STAMFORD ST.j S.E. I, 
AND BUNGAY, SUFFOLK. 







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